Affirmative action

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Language: en

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- [Instructor] What we're
going to do in this video

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is discuss affirmative action

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and it can be a sensitive topic,

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so I encourage folks to
engage on the message boards

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but to do so respectfully.

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So, the first question is
what is affirmative action?

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So, generally speaking you could view it

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as efforts to improve opportunities

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for underrepresented groups

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and oftentimes it will be
for underrepresented racial

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or ethnic groups or for women.

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To help us think through
the types of efforts

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that might be classified

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or that might be associated
with affirmative action

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we can set up a little
bit of a spectrum here.

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At one end of the spectrum

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you could have outright quotas.

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These could be situations

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where say a university
admissions department

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says we're going to say 10% of our class

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is gonna be from this
group or from that group.

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In between you could have race
or gender-aware admissions

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where it is a factor in admissions.

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Race/gender is a factor.

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And at this end of the spectrum

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there's outreach to groups

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to make sure that people
who could be qualified

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who are from underrepresented
groups are applying,

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so this would be outreach.

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Now, in popular language today,

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affirmative action
tends to refer to things

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more on this end of the spectrum

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and the phrase affirmative action

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first comes into popular usage

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during Lyndon B. Johnson's presidency.

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Now, as you can imagine

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this is a very sensitive topic

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because on one hand

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folks could say yes,

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it would be nice to give opportunity

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for folks who historically
have not had opportunity

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or folks who are
historically underrepresented

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but other people might say

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well, shouldn't we be
a race blind society?

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If you are factoring race for one group,

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well, doesn't that hurt another group

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and couldn't it cause
reverse discrimination?

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And to appreciate the legal history here,

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we can go back to 1978

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where we have the case
Regents of the University

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of California v. Bakke in the
United States Supreme Court

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and this is a situation

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where Bakke is a former
solider and engineer

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who also happens to be white

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who wants to go to medical school.

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He gets rejected by the
University of California

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at Davis and he claims

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that there was reverse
discrimination at play

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because they had a quota system.

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16 out of the 100 seats
at the medical school

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were reserved for
underrepresented minorities

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and the Supreme Court actually had trouble

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deciding on this case.

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It was a very divided opinion

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and eventually Justice Powell's opinion

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became the opinion that
people paid attention to.

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And it was a little bit mixed.

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It said that outright
quotas are unconstitutional

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and that Bakke should be allowed admission

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and he was able to go

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to University of California,
Davis Medical School

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but Justice Powell tried
to thread the needle

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by saying even though quotas

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might be unconstitutional

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it is okay to consider race
as a factor in admissions

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especially if it's being used
for the educational benefit

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of diversity of the community.

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In 1996 the voters of California

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actually voted directly on this issuer

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and they passed the California
Civil Rights Initiative

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more commonly know as Proposition 209

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and this proposition made it illegal

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to consider race, sex or
ethnicity when it came

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to government jobs or admissions

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in state schools.

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It has been challenged by
proponents of affirmative action

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many time but all of those challenges

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have been unsuccessful to date.

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These issues surface
again in the Supreme Court

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in 2003 when we get to the
Grutter versus Bollinger case.

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This case has some
parallels to the Bakke case.

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In this case Grutter is a white applicant

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to the University of Michigan Law School

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who claims that she was denied admission

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because the Law School was
giving racial preference

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which was causing essentially
reverse discrimination.

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The Supreme Court rules against Grutter

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but it's really interesting
to read the majority opinion

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written by Sandra Day O'Connor

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and the dissenting opinion
from Clarence Thomas

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because it gives us some texture

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into the nuances of these decisions.

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Here is an excerpt

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from Sandra Day O'Connor's
majority opinion.

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We last addressed the use of race

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in public higher education
over 25 years ago.

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In the landmark Bakke case,

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we reviewed a racial set-aside program

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that reserves 16 out of 100 seats

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in a medical school class

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for members of certain minority groups.

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Since this Court's
splinter decision in Bakke,

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Justice Powell's opinion

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announcing the judgment of the court

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has served as the touchstone
for constitutional analysis

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of race-conscious admissions policies.

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And then she goes on to list

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the situations that Justice Powell

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said were not okay to justify race

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as a factor in admissions.

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Justice Powell rejected an interest

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in reducing the historic deficit

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of traditionally disfavored minorities

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in medical schools

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and in the medical profession

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as an unlawful interest
in racial balancing.

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So, according to Justice
Powell in the Bakke case,

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you can't justify
race-conscious admissions

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to try to fix historic deficits.

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Sandra Day O'Connor goes on to write

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Justice Powell in the Bakke case

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rejected an interest in
remedying societal discrimination

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because such measures would risk placing

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unnecessary burdens on
innocent third parties

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who bare no responsibility

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for whatever harm the beneficiaries

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of the special admissions program

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are thought to have suffered.

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So, you also can't have
race-conscious admissions

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if the goal is to remedy
current societal discrimination

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because if you're benefiting someone,

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you're also putting the burden on people

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who might have nothing to do

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with that societal discrimination.

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And then she goes on to write

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that in the Bakke case Justice Powell

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approved the university's
use and here we're talking

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about the University of California's use

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of race to further only one interest,

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the attainment of a diverse student body.

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And now in this part of the excerpt

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she shifts to talking
about the case at hand

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in Grutter versus Bollinger

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where we're talking about admissions

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to the University of Michigan Law School.

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As part of its goal of assembling a class

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that is both exceptionally
academically qualified

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and broadly diverse,

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the Law School seeks to enroll

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a critical mass of minority students.

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The Law School's concept of critical mass

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is defined by reference to
the educational benefits

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that diversity is designed to produce.

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These benefits are substantial.

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As the district court emphasized

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the Law School's
admissions policy promotes

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cross-racial understanding,

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helps to break down racial stereotypes

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and enables students to better understand

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persons of different races.

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We, the majority in the Supreme Court,

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agree that in the context of
its individualized inquiry

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into the possible diversity contributions

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of all applicants,

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the Law School's race-conscious
admissions program

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does not unduly harm
non-minority applicants.

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In summary, the Equal Protection Clause

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of the 14th Amendment

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does not prohibit the Law
School's narrowly tailored use

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of race in admissions decisions

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to further a compelling interest

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in obtaining the educational benefits

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that flow from a diverse student body.

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So, in this situation the majority opinion

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that's penned by Justice O'Connor

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is clarifying Powell's statement in Bakke

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saying that diversity is a
legitimate educational benefit

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that universities can optimize around

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as long as race is one of many factors

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in the admissions process.

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Now, on the other hand,

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you have the dissenting opinion

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from Justice Clarence Thomas.

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Here is an excerpt he wrote.

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I believe blacks can
achieve in every avenue

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of American life without the meddling

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of university administrators.

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Because I wish to see all students succeed

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whatever their color,

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I share in some respect the sympathies

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of those who sponsor the
type of discrimination

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advanced by the University
of Michigan Law School.

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The Constitution does
not, however, tolerate

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institutional devotion to the status quo

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in admissions policies

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when such devotion ripens
into racial discrimination.

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So, he's calling the University
of Michigan Law School's

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admissions policies
outright discrimination.

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He's saying that look,

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even though it might be the status quo,

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it's essentially what
a lot of universities

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have been doing since Bakke.

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It's not okay because it has ripened

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into racial discrimination.

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The majority, he's
talking about the majority

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of the Supreme Court upholds

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the Law School's racial discrimination

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not by interpreting the
people's Constitution,

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so the US Constitution

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but by responding to a faddish slogan

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of the cognoscenti.

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So, here he's making reference
to this idea of diversity

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which he's calling a faddish
slogan of the cognoscenti.

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Cognoscenti would be people

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who are in the know,

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or people who think they're in the know.

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Nevertheless, I concur in part

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in the Court's opinion.

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I agree with the Court's holding

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that racial discrimination in
higher education admissions

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will be illegal in 25 years.

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And here he's making reference

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that in Sandra Day O'Connor's opinion

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she did say that in 25 years

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it might not be okay to have
race-conscious admissions.

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I respectfully dissent

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from the remainder of the Court's opinion

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and the judgment, however,

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because I believe that the
Law School's current use

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of race violates the
Equal Protection Clause

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and that the Constitution
means the same thing today

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as it will in 300 months.

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So, here he's saying look,

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if the majority thinks
that it's right now okay

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to have race-conscious admissions

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but it's not okay in 25 years,

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well, what's gonna change
about the Constitution?

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If it's going to be
unconstitutional in 25 years,

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it should be unconstitutional today.

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Finally, he goes on to say

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the Constitution abhors
classifications based on race

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not only because those classifications

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can harm favored races

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or are based on illegitimate motives

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but also because every time
the government places citizens

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on racial registers

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and makes race relevant to
the provision of burdens

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or benefits, it demeans us all.

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I encourage you to think about it.

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Are you more on the side of Justice Powell

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or Sandra Day O'Connor

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where race is a legitimate
factor in admissions

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especially if it's in service

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to diversity which is considered

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a benefit for an educational community

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or you more on the side of Justice Thomas

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and Proposition 209 in California

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saying that look, we need
to be racially blind.

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The 14th Amendment, the
Equal Protection Clause

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of the 14th Amendment says

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that we should be a racially blind country

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and that every time we
try to involve race,

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it might do more harm than good.

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You decide.


Rulings on majority and minority rights by the Supreme Court

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Language: en

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- We've already talked
about the 14th Amendment

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in previous videos,
but just as a reminder,

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Section 1 of the 14th Amendment says,

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"All persons born or naturalized
in the United States,

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"and subject to the jurisdiction thereof,

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"are citizens of the United States

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"and of the State wherein they reside.

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"No State shall make or enforce any law

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"which shall abridge the
privileges or immunities

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"of citizens of the United States;

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"nor shall any State deprive any person

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"of life, liberty, or property,

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"without the due process of law;

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"nor deny to any person
within its jurisdiction

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"the equal protection of the laws."

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And this last clause,
which I just underlined,

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the Equal Protection Clause,
has been cited many times,

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not just in social justice movements

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but in many Supreme Court cases.

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And what we're going to do in this video

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is think about how rulings
by the Supreme Court

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represent both continuity over time,

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but also change over
time, especially relative

00:01:00.080 --> 00:01:03.330
to the protection of minority rights.

00:01:03.330 --> 00:01:05.360
One of the most significant test cases

00:01:05.360 --> 00:01:08.490
of the 14th Amendment
happens almost 30 years

00:01:08.490 --> 00:01:12.420
after the amendment is ratified in 1896.

00:01:12.420 --> 00:01:14.970
This is a situation where
the state of Louisiana

00:01:14.970 --> 00:01:18.340
passes a law that African American people

00:01:18.340 --> 00:01:22.270
have to sit in a separate
railcar from white people.

00:01:22.270 --> 00:01:23.970
And so you have this gentleman here,

00:01:23.970 --> 00:01:26.940
Homer Plessy, a resident of New Orleans,

00:01:26.940 --> 00:01:29.970
who decides to test this law.

00:01:29.970 --> 00:01:32.630
He sits in a white only car,

00:01:32.630 --> 00:01:34.840
and he is 1/8 African American.

00:01:34.840 --> 00:01:36.920
And he gets arrested.

00:01:36.920 --> 00:01:38.480
This case eventually goes to

00:01:38.480 --> 00:01:40.000
the United States Supreme Court,

00:01:40.000 --> 00:01:42.700
and they rule that the Louisiana law

00:01:42.700 --> 00:01:46.740
requiring separate cars
is not unconstitutional

00:01:46.740 --> 00:01:50.460
as long as the cars
are judged to be equal.

00:01:50.460 --> 00:01:54.050
And this is where that term
"separate but equal" comes from.

00:01:54.050 --> 00:01:57.950
And this is viewed as a
fairly infamous ruling

00:01:57.950 --> 00:02:01.120
because it was the
Supreme Court reinforcing

00:02:01.120 --> 00:02:04.760
this idea of segregation, even after

00:02:04.760 --> 00:02:08.840
the 14th Amendment had been
passed almost 30 years prior.

00:02:08.840 --> 00:02:12.030
Now, we go almost 60 years in the future

00:02:12.030 --> 00:02:14.870
in order for segregation to be challenged

00:02:14.870 --> 00:02:16.950
in a very significant way.

00:02:16.950 --> 00:02:19.010
Then we get to the case of Brown versus

00:02:19.010 --> 00:02:23.030
Board of Education of
Topeka, Kansas in 1954,

00:02:23.030 --> 00:02:24.940
in which the then Supreme Court

00:02:24.940 --> 00:02:28.247
rules that "No, segregation is not okay.

00:02:28.247 --> 00:02:31.370
"Separate is inherently unequal."

00:02:31.370 --> 00:02:33.250
And this right over here is a picture

00:02:33.250 --> 00:02:35.740
of a desegregated
classroom around that time

00:02:35.740 --> 00:02:37.790
although this is not in Topeka, Kansas.

00:02:37.790 --> 00:02:41.200
But it shows how based
on the passage of time,

00:02:41.200 --> 00:02:44.100
based on social norms, based on a change

00:02:44.100 --> 00:02:46.000
in the make-up of the Supreme Court,

00:02:46.000 --> 00:02:49.400
how they can make rulings
that go one way or the other.

00:02:49.400 --> 00:02:52.840
Plessy versus Ferguson
reaffirms segregation.

00:02:52.840 --> 00:02:56.070
It's perceived to curtail minority rights

00:02:56.070 --> 00:02:58.850
while Brown versus Board of
Education goes the other way.

00:02:58.850 --> 00:03:02.700
Once again, taking a look
at the 14th Amendment.

00:03:02.700 --> 00:03:04.960
Now, if we fast-forward to 1993,

00:03:04.960 --> 00:03:06.880
we have another really interesting

00:03:06.880 --> 00:03:09.760
test case, Shaw versus Reno.

00:03:09.760 --> 00:03:12.770
This is a situation where
after the 1990 census

00:03:12.770 --> 00:03:16.200
North Carolina takes a look
at its congressional districts

00:03:16.200 --> 00:03:20.190
and sends them to review by
the federal Justice Department.

00:03:20.190 --> 00:03:22.010
The federal Justice Department decides

00:03:22.010 --> 00:03:24.300
that the first pass
that North Carolina took

00:03:24.300 --> 00:03:27.030
at the districting only had one

00:03:27.030 --> 00:03:29.430
black majority congressional district.

00:03:29.430 --> 00:03:31.010
And they thought that there could be

00:03:31.010 --> 00:03:33.930
two black majority
congressional districts.

00:03:33.930 --> 00:03:36.620
So, the state of North
Carolina redistricted again,

00:03:36.620 --> 00:03:38.690
and they created this 12th district here,

00:03:38.690 --> 00:03:41.500
which you can see is
kind of a strange shape.

00:03:41.500 --> 00:03:46.500
It's strung along over 160 miles
in this very thin district.

00:03:47.030 --> 00:03:49.550
Now, this was taken to the Supreme Court

00:03:49.550 --> 00:03:51.610
by citizens of North Carolina saying that

00:03:51.610 --> 00:03:54.420
this districting was a severe
case of gerrymandering,

00:03:54.420 --> 00:03:55.810
which we've talked about in other videos,

00:03:55.810 --> 00:03:57.950
and should be deemed unconstitutional.

00:03:57.950 --> 00:04:01.560
And the Supreme Court
actually did rule in 1993

00:04:01.560 --> 00:04:05.010
that redistricting purely
on the basis of race,

00:04:05.010 --> 00:04:06.580
as was done in this situation,

00:04:06.580 --> 00:04:09.600
even though it was with the intent

00:04:09.600 --> 00:04:12.580
of having more minority representation

00:04:12.580 --> 00:04:14.950
in Congress, that this
type of redistricting

00:04:14.950 --> 00:04:18.210
on the basis of race was unconstitutional.

00:04:18.210 --> 00:04:21.650
This Supreme Court also cited
the Equal Protection Clause

00:04:21.650 --> 00:04:23.987
and also cited the 14th Amendment saying,

00:04:23.987 --> 00:04:26.747
"Look, once you start redistricting

00:04:26.747 --> 00:04:29.547
"based on racial lines, it creates a type

00:04:29.547 --> 00:04:33.017
"of racial separation,
which is unconstitutional

00:04:33.017 --> 00:04:35.360
"by the 14th Amendment."

00:04:35.360 --> 00:04:38.080
So, these are really good cases to know.

00:04:38.080 --> 00:04:40.610
They show how the Supreme Court

00:04:40.610 --> 00:04:42.090
can rule differently depending

00:04:42.090 --> 00:04:43.850
on what time period we are in

00:04:43.850 --> 00:04:46.080
or depending on the circumstance.

00:04:46.080 --> 00:04:48.030
That often times when we think about

00:04:48.030 --> 00:04:49.597
equal protection, we think about

00:04:49.597 --> 00:04:52.060
protection of minority rights.

00:04:52.060 --> 00:04:54.590
But as we saw in the
case of Shaw versus Reno,

00:04:54.590 --> 00:04:57.760
even when the intent of, in
this case gerrymandering,

00:04:57.760 --> 00:05:01.180
is to give more minority representation,

00:05:01.180 --> 00:05:03.290
it was deemed unconstitutional

00:05:03.290 --> 00:05:05.190
because from the Supreme Court's

00:05:05.190 --> 00:05:07.693
point of view violated the 14th Amendment.


Letter from a Birmingham Jail

WEBVTT
Kind: captions
Language: en

00:00:00.210 --> 00:00:01.670
- [Narrator] What we're
going to read together

00:00:01.670 --> 00:00:04.720
in this video is what has become known as

00:00:04.720 --> 00:00:07.870
Martin Luther King's Letter
from a Birmingham Jail,

00:00:07.870 --> 00:00:11.860
which he wrote from a jail cell in 1963

00:00:11.860 --> 00:00:14.020
after he and several of his associates

00:00:14.020 --> 00:00:16.580
were arrested in Birmingham, Alabama

00:00:16.580 --> 00:00:20.790
as they nonviolently
protested segregation there.

00:00:20.790 --> 00:00:22.810
And, I'm going to read an excerpt of it.

00:00:22.810 --> 00:00:25.300
I encourage you to read
it in its entirety.

00:00:25.300 --> 00:00:27.040
It is one of the most powerful documents,

00:00:27.040 --> 00:00:28.480
frankly, I have ever read.

00:00:28.480 --> 00:00:30.210
And Martin Luther King often gets

00:00:30.210 --> 00:00:31.980
a lot of credit as an amazing speaker.

00:00:31.980 --> 00:00:33.537
People say, "Hey, he
could read the phone book,

00:00:33.537 --> 00:00:34.760
"and it would move people."

00:00:34.760 --> 00:00:37.750
But this also speaks to what
an incredible writer he was.

00:00:37.750 --> 00:00:40.260
Not only is it moving, but it really gives

00:00:40.260 --> 00:00:42.450
the philosophical underpinnings of the

00:00:42.450 --> 00:00:44.680
Civil Rights Movement of the 1960s.

00:00:44.680 --> 00:00:48.500
And many people attribute
the Civil Rights Act of 1964

00:00:48.500 --> 00:00:51.310
passed by Congress as
being heavily influenced

00:00:51.310 --> 00:00:53.100
by Martin Luther King's letter.

00:00:53.100 --> 00:00:55.160
Now, what motivated Martin Luther King

00:00:55.160 --> 00:00:57.270
to write this letter was a statement

00:00:57.270 --> 00:01:00.680
made in the newspaper by
eight Alabama clergymen,

00:01:00.680 --> 00:01:03.270
which encouraged the protesters to wait

00:01:03.270 --> 00:01:06.217
saying, "That, yes, we are
sympathetic to the injustices,

00:01:06.217 --> 00:01:07.867
"but they should be resolved in the courts

00:01:07.867 --> 00:01:10.027
"and not through the type of protests,

00:01:10.027 --> 00:01:12.267
"the type of tension,
that Martin Luther King

00:01:12.267 --> 00:01:14.650
"and his fellow protesters were creating."

00:01:14.650 --> 00:01:16.690
And so, here's just an excerpt of what

00:01:16.690 --> 00:01:18.557
Martin Luther King wrote,

00:01:18.557 --> 00:01:21.717
"You may well ask, 'Why direct action?

00:01:21.717 --> 00:01:24.546
"'Why sit ins, marches and so forth?

00:01:24.546 --> 00:01:27.097
"'Isn't negotiation a better path?'

00:01:27.097 --> 00:01:30.297
"You are quite right in
calling for negotiation.

00:01:30.297 --> 00:01:33.937
"Indeed, this is the very
purpose of direct action.

00:01:33.937 --> 00:01:37.167
"Nonviolent direct action seeks to create

00:01:37.167 --> 00:01:40.047
"such a crisis and foster such a tension

00:01:40.047 --> 00:01:42.727
"that a community which
has constantly refused

00:01:42.727 --> 00:01:46.587
"to negotiate is forced
to confront the issue.

00:01:46.587 --> 00:01:48.927
"It seeks so to dramatize the issue

00:01:48.927 --> 00:01:51.357
"that it can no longer be ignored.

00:01:51.357 --> 00:01:53.427
"My citing the creation of tension

00:01:53.427 --> 00:01:56.107
"as part of the work of
the nonviolent resister

00:01:56.107 --> 00:01:58.367
"may sound rather shocking.

00:01:58.367 --> 00:02:00.247
"But I must confess that I am

00:02:00.247 --> 00:02:03.207
"not afraid of the word 'tension.'

00:02:03.207 --> 00:02:06.547
"I have earnestly opposed violent tension,

00:02:06.547 --> 00:02:08.797
"but there is a type of constructive,

00:02:08.797 --> 00:02:12.333
"nonviolent tension which
is necessary for growth.

00:02:13.557 --> 00:02:16.187
"Just as Socrates felt
that it was necessary

00:02:16.187 --> 00:02:18.277
"to create a tension in the mind so that

00:02:18.277 --> 00:02:20.857
"individuals could rise from the bondage

00:02:20.857 --> 00:02:23.917
"of myths and half truths
to the unfettered realm

00:02:23.917 --> 00:02:26.707
"of creative analysis
and objective appraisal,

00:02:26.707 --> 00:02:30.687
"so must we see the need
for nonviolent gadflies

00:02:30.687 --> 00:02:33.277
"to create the kind of tension in society

00:02:33.277 --> 00:02:36.097
"that will help men rise
from the dark depths

00:02:36.097 --> 00:02:39.317
"of prejudice and racism
to the majestic heights

00:02:39.317 --> 00:02:41.687
"of understanding and brotherhood.

00:02:41.687 --> 00:02:44.567
"The purpose of our direct action program

00:02:44.567 --> 00:02:47.707
"is to create a situation so crisis packed

00:02:47.707 --> 00:02:51.323
"that it will inevitably
open the door to negotiation.

00:02:52.347 --> 00:02:55.007
"I guess it is easy for
those who have never felt

00:02:55.007 --> 00:02:58.557
"the stinging darts of
segregation to say 'wait.'

00:02:58.557 --> 00:03:00.427
"But when you have seen vicious mobs

00:03:00.427 --> 00:03:02.627
"lynch your mothers and fathers at will

00:03:02.627 --> 00:03:05.567
"and drown your sister
and brothers at whim;

00:03:05.567 --> 00:03:07.597
"when you have seen hate-filled policemen

00:03:07.597 --> 00:03:09.957
"curse, kick, brutalize, and even kill

00:03:09.957 --> 00:03:12.677
"your black brothers and
sisters with impunity;

00:03:12.677 --> 00:03:15.777
"when you see the vast
majority of your 20 million

00:03:15.777 --> 00:03:19.067
"Negro brothers smothering
in an airtight cage

00:03:19.067 --> 00:03:22.387
"of poverty in the midst
of an affluent society;

00:03:22.387 --> 00:03:24.417
"when you suddenly find
your tongue twisted

00:03:24.417 --> 00:03:27.217
"and your speech stammering
as you seek to explain

00:03:27.217 --> 00:03:29.717
"to your six-year-old
daughter why she cannot go

00:03:29.717 --> 00:03:31.637
"to the public amusement park that has

00:03:31.637 --> 00:03:34.247
"just been advertised on television;

00:03:34.247 --> 00:03:36.087
"when you take a cross-country drive

00:03:36.087 --> 00:03:38.747
"and find it necessary to
sleep night after night

00:03:38.747 --> 00:03:41.407
"in the uncomfortable
corners of your automobile

00:03:41.407 --> 00:03:43.857
"because no motel will accept you;

00:03:43.857 --> 00:03:46.397
"when you are humiliated
day in and day out

00:03:46.397 --> 00:03:49.757
"by nagging signs reading
'white' and 'colored,'

00:03:49.757 --> 00:03:54.757
"then you will understand why
we find it difficult to wait."

00:03:55.810 --> 00:03:58.430
I've read this many times,
but every time I read it,

00:03:58.430 --> 00:04:00.810
and this is just an
excerpt, as you can tell,

00:04:00.810 --> 00:04:01.960
it's incredibly powerful.

00:04:01.960 --> 00:04:04.420
And I encourage you to
read it in its entirety,

00:04:04.420 --> 00:04:07.100
and think about why this was
such a powerful document,

00:04:07.100 --> 00:04:08.710
especially for catalyzing things

00:04:08.710 --> 00:04:11.353
like the Civil Rights Act of 1964.


The Fourteenth Amendment and equal protection

WEBVTT
Kind: captions
Language: en

00:00:00.160 --> 00:00:00.993
- [Instructor] Many parts of

00:00:00.993 --> 00:00:02.930
the United States Constitution deal

00:00:02.930 --> 00:00:04.550
with rights of an individual,

00:00:04.550 --> 00:00:07.010
and many amendments talk about protecting

00:00:07.010 --> 00:00:09.620
or expanding the rights of an individual,

00:00:09.620 --> 00:00:11.850
but the 14th Amendment is perhaps one

00:00:11.850 --> 00:00:14.900
of the most important
amendments in this discussion

00:00:14.900 --> 00:00:16.920
of protecting civil rights.

00:00:16.920 --> 00:00:20.090
And, in particular, Section 1 is the part

00:00:20.090 --> 00:00:21.900
that is most cited.

00:00:21.900 --> 00:00:23.507
So, let's just read this together.

00:00:23.507 --> 00:00:26.637
"All persons born or naturalized
in the United States,

00:00:26.637 --> 00:00:29.087
"and subject to the jurisdiction thereof,

00:00:29.087 --> 00:00:30.997
"are citizens of the United States

00:00:30.997 --> 00:00:34.037
"and of the state wherein they reside.

00:00:34.037 --> 00:00:37.727
"No state shall make or enforce any law

00:00:37.727 --> 00:00:39.577
"which shall abridge the privileges

00:00:39.577 --> 00:00:42.637
"or immunities of citizens
of the United States,

00:00:42.637 --> 00:00:46.507
"nor shall any state
deprive any person of life,

00:00:46.507 --> 00:00:50.787
"liberty, or property,
without due process of law,

00:00:50.787 --> 00:00:54.547
"nor deny to any person
within its jurisdiction

00:00:54.547 --> 00:00:57.870
"the equal protection of the laws."

00:00:57.870 --> 00:01:00.470
So, let's just focus in on parts of it.

00:01:00.470 --> 00:01:03.930
So, one big takeaway
about the 14th Amendment,

00:01:03.930 --> 00:01:05.507
this is the federal government saying,

00:01:05.507 --> 00:01:08.430
"Hey, these are things
that the state cannot do."

00:01:08.430 --> 00:01:10.257
So, for example, when it says,

00:01:10.257 --> 00:01:14.387
"Nor shall any state
deprive any person of life,

00:01:14.387 --> 00:01:18.440
"liberty, or property,
without due process of law,"

00:01:18.440 --> 00:01:20.570
this is a restatement
of the 5th Amendment,

00:01:20.570 --> 00:01:22.167
that, "Hey, you know,
people can't just stick you

00:01:22.167 --> 00:01:25.107
"in jail or take away your
property without you going

00:01:25.107 --> 00:01:28.590
"through some type of a
process, a legal process."

00:01:28.590 --> 00:01:30.790
Well, in the 5th Amendment,
this was really talking about

00:01:30.790 --> 00:01:32.340
the federal government not being able

00:01:32.340 --> 00:01:35.020
to just take your property
or your liberty away

00:01:35.020 --> 00:01:36.930
from you without the process of law,

00:01:36.930 --> 00:01:40.070
but here, it's saying,
"Nor shall any state."

00:01:40.070 --> 00:01:41.540
And this clause right over here,

00:01:41.540 --> 00:01:44.440
this is known as the due process clause

00:01:44.440 --> 00:01:46.220
of the 14th Amendment.

00:01:46.220 --> 00:01:47.327
Then, right after that, it says,

00:01:47.327 --> 00:01:51.397
"Nor deny to any person
within its jurisdiction

00:01:51.397 --> 00:01:54.047
"the equal protection of the laws.

00:01:54.047 --> 00:01:55.680
"The equal protection of the laws,"

00:01:55.680 --> 00:01:56.990
I'm gonna underline that.

00:01:56.990 --> 00:01:58.760
And this, you might guess is called

00:01:58.760 --> 00:02:01.450
the equal protection clause.

00:02:01.450 --> 00:02:05.070
Now, the context in which the
14th Amendment was ratified,

00:02:05.070 --> 00:02:07.950
it happens in 1868,

00:02:07.950 --> 00:02:10.620
shortly after the end of the Civil War.

00:02:10.620 --> 00:02:12.400
You, of course, have
the 13th Amendment that,

00:02:12.400 --> 00:02:15.040
among other things, abolishes slavery,

00:02:15.040 --> 00:02:16.280
but then, you have these things

00:02:16.280 --> 00:02:18.230
in the south called black codes,

00:02:18.230 --> 00:02:21.690
which continue to repress the
rights of African-Americans,

00:02:21.690 --> 00:02:24.270
and that's why Congress felt the need

00:02:24.270 --> 00:02:26.840
for the 14th Amendment to be passed.

00:02:26.840 --> 00:02:28.680
Now, one of the most notable cases

00:02:28.680 --> 00:02:32.913
in which the 14th Amendment
was brought up happens in 1896,

00:02:34.391 --> 00:02:36.360
Plessy v. Ferguson,

00:02:36.360 --> 00:02:38.970
and we have a whole video about this.

00:02:38.970 --> 00:02:41.090
And this is a case in which it was argued

00:02:41.090 --> 00:02:44.300
that is was unconstitutional
under the 14th Amendment

00:02:44.300 --> 00:02:47.020
for African-Americans to have to travel

00:02:47.020 --> 00:02:50.150
in a separate train car
from white Americans,

00:02:50.150 --> 00:02:52.737
and the Supreme Court
infamously said that,

00:02:52.737 --> 00:02:54.827
"Hey, as long as it is equal,

00:02:54.827 --> 00:02:56.717
"it is okay for it to be separate

00:02:56.717 --> 00:02:59.850
"and that it would not
violate the 14th Amendment,"

00:02:59.850 --> 00:03:04.143
and so, this idea of separate
but equal comes about.

00:03:05.790 --> 00:03:07.490
Now, that was significantly challenged

00:03:07.490 --> 00:03:09.890
as we go into 1954,

00:03:09.890 --> 00:03:12.630
where you have Brown v. Board of Education

00:03:12.630 --> 00:03:14.520
of Topeka, Kansas.

00:03:14.520 --> 00:03:16.833
Board of Education.

00:03:17.740 --> 00:03:21.000
And here, the argument
was that, inherently,

00:03:21.000 --> 00:03:23.140
separate could not be equal,

00:03:23.140 --> 00:03:26.600
and once again, the 14th
Amendment was invoked.

00:03:26.600 --> 00:03:29.580
And this time, the Supreme
Court unanimously ruled that,

00:03:29.580 --> 00:03:32.050
yes, separate can't be equal,

00:03:32.050 --> 00:03:35.450
and that the schools
needed to be desegregated.

00:03:35.450 --> 00:03:37.970
So, even though it wasn't
an official overruling

00:03:37.970 --> 00:03:41.710
of Plessy v. Ferguson, it
was a functional overruling

00:03:41.710 --> 00:03:44.800
of this doctrine of separate but equal.

00:03:44.800 --> 00:03:47.810
And, as we go into the
1960s civil rights movement,

00:03:47.810 --> 00:03:49.810
led by folks like Martin Luther King,

00:03:49.810 --> 00:03:52.500
it was the 14th Amendment
that was cited often.

00:03:52.500 --> 00:03:53.620
In another video, we're going to look

00:03:53.620 --> 00:03:56.960
at Martin Luther King's
letter from a Birmingham jail,

00:03:56.960 --> 00:03:59.140
in which he articulates the ideas

00:03:59.140 --> 00:04:01.880
of the civil rights movement,
it's a quite moving letter.

00:04:01.880 --> 00:04:04.410
But, once again, it's evoking these ideas

00:04:04.410 --> 00:04:07.730
of the 14th Amendment,
and it goes onto movements

00:04:07.730 --> 00:04:11.090
as disparate as the
women's rights movement,

00:04:11.090 --> 00:04:12.430
led by organizations like

00:04:12.430 --> 00:04:14.270
the National Organization for Women,

00:04:14.270 --> 00:04:16.300
citing equal protection of the laws

00:04:16.300 --> 00:04:19.660
in situations of sexual
discrimination in the workplace.

00:04:19.660 --> 00:04:22.710
You have pro-life groups
citing the 14th Amendment,

00:04:22.710 --> 00:04:25.890
arguing that an unborn
fetus' right to life

00:04:25.890 --> 00:04:28.710
is protected by the 14th Amendment.

00:04:28.710 --> 00:04:30.850
You have rulings around whether quotas

00:04:30.850 --> 00:04:33.860
in higher education are legal or not,

00:04:33.860 --> 00:04:38.680
once again, citing ideas of
equal protection of the laws.

00:04:38.680 --> 00:04:40.560
So, as you go forth in your study

00:04:40.560 --> 00:04:43.420
of United States government,
the 14th Amendment,

00:04:43.420 --> 00:04:46.623
especially Section 1, is
going to keep showing up.


Energy graphs for simple harmonic motion

WEBVTT
Kind: captions
Language: en

00:00:00.350 --> 00:00:01.930
- [Instructor] What I have drawn here,

00:00:01.930 --> 00:00:05.570
is a mass sitting on
a frictionless surface

00:00:05.570 --> 00:00:09.350
that is attached to a spring
that is attached to the wall,

00:00:09.350 --> 00:00:10.650
and what we're going to do is

00:00:10.650 --> 00:00:12.960
we're going to compress the spring.

00:00:12.960 --> 00:00:15.310
We're going to get the mass to position A.

00:00:15.310 --> 00:00:17.030
Right now it's at position zero.

00:00:17.030 --> 00:00:19.180
We're going to get it to position A.

00:00:19.180 --> 00:00:23.100
And then at time equals
zero, we are going to let go.

00:00:23.100 --> 00:00:25.040
And so you can imagine
what's going to happen,

00:00:25.040 --> 00:00:27.420
especially with this mass
on a frictionless surface.

00:00:27.420 --> 00:00:29.570
It's going to oscillate between position A

00:00:29.570 --> 00:00:31.270
and position negative A,

00:00:31.270 --> 00:00:33.530
and we have that depicted right here

00:00:33.530 --> 00:00:36.290
on this position versus time graph.

00:00:36.290 --> 00:00:39.250
It'll start at position A,
and then it will oscillate

00:00:39.250 --> 00:00:41.130
to the left to position negative A

00:00:41.130 --> 00:00:44.940
and then oscillate to the
right to position A again,

00:00:44.940 --> 00:00:46.690
on and on and on forever,

00:00:46.690 --> 00:00:48.580
if we're dealing with a
world that is frictionless.

00:00:48.580 --> 00:00:49.560
Like I said, frictionless surface,

00:00:49.560 --> 00:00:52.700
and let's also assume no air resistance.

00:00:52.700 --> 00:00:54.800
So that is all very interesting,

00:00:54.800 --> 00:00:56.390
but what we want to think
about in this video is

00:00:56.390 --> 00:00:59.430
how that might relate to energy.

00:00:59.430 --> 00:01:02.240
So given the information
that I've just given you,

00:01:02.240 --> 00:01:05.820
let's start thinking about
elastic potential energy.

00:01:05.820 --> 00:01:09.030
Remember, at time equals zero,
the box is at position A,

00:01:09.030 --> 00:01:10.580
so our spring is compressed.

00:01:10.580 --> 00:01:13.490
And we're dealing with
a box-spring system,

00:01:13.490 --> 00:01:16.660
so the combined system of
the box and the spring.

00:01:16.660 --> 00:01:19.890
And we're going to assume
that there is no added energy

00:01:19.890 --> 00:01:22.910
that's added to or taken
away from this system.

00:01:22.910 --> 00:01:26.050
So right at time zero, when
we have the spring compressed,

00:01:26.050 --> 00:01:28.020
that box-spring system is gonna have

00:01:28.020 --> 00:01:30.620
some elastic potential energy.

00:01:30.620 --> 00:01:32.640
And so let's put that right over there.

00:01:32.640 --> 00:01:35.810
And then what's going to
happen when we let go?

00:01:35.810 --> 00:01:37.890
Well, the box is going to be pushed

00:01:37.890 --> 00:01:40.010
by the spring towards the left.

00:01:40.010 --> 00:01:41.800
Actually, is going to be
accelerated to the left.

00:01:41.800 --> 00:01:45.460
And right when the box crosses
the x position of zero,

00:01:45.460 --> 00:01:48.380
which we see happens at
time equals one second,

00:01:48.380 --> 00:01:50.290
all of our potential energy

00:01:50.290 --> 00:01:52.960
is going to be converted
to kinetic energy.

00:01:52.960 --> 00:01:56.460
And so our potential energy is
going to be right over here.

00:01:56.460 --> 00:01:58.430
And then what happens is the box

00:01:58.430 --> 00:02:01.550
starts getting decelerated by the spring,

00:02:01.550 --> 00:02:04.180
and it gets to position negative A.

00:02:04.180 --> 00:02:05.470
Well, at position negative A,

00:02:05.470 --> 00:02:09.260
which we see happens at
time equals two seconds,

00:02:09.260 --> 00:02:10.810
well, then we are back to having

00:02:10.810 --> 00:02:13.090
our maximum potential energy again.

00:02:13.090 --> 00:02:15.770
So we're back to having our
maximum potential energy

00:02:15.770 --> 00:02:17.880
at time equals two seconds,

00:02:17.880 --> 00:02:21.240
with is associated with
being at position negative A.

00:02:21.240 --> 00:02:23.210
And so you can see where this is going.

00:02:23.210 --> 00:02:26.100
At three seconds, all of that
potential energy is back,

00:02:26.100 --> 00:02:27.320
converted to kinetic energy.

00:02:27.320 --> 00:02:29.850
At four seconds, we
are back at position A.

00:02:29.850 --> 00:02:31.700
It's back into potential energy again.

00:02:31.700 --> 00:02:34.820
And so the graph of our
elastic potential energy

00:02:34.820 --> 00:02:38.900
is going to look something like this.

00:02:38.900 --> 00:02:41.210
It's going to look something like,

00:02:41.210 --> 00:02:45.100
this is a hand-drawn version
of it, but you, I think,

00:02:45.100 --> 00:02:47.800
get the general idea of
what's going on here.

00:02:47.800 --> 00:02:50.133
Notice it is not getting negative,

00:02:51.000 --> 00:02:53.170
and so it would look something like that.

00:02:53.170 --> 00:02:54.680
Now what about kinetic energy?

00:02:54.680 --> 00:02:56.710
Well, I've already made
some reference to it,

00:02:56.710 --> 00:02:59.640
but let's think about how
that would trend over time.

00:02:59.640 --> 00:03:03.880
At time equal zero, when
the box is at position A,

00:03:03.880 --> 00:03:05.160
right at that moment,

00:03:05.160 --> 00:03:08.840
we aren't going to have any
kinetic energy just yet.

00:03:08.840 --> 00:03:10.850
But then the box is
going to be accelerated

00:03:10.850 --> 00:03:13.790
as that potential energy is
turned into kinetic energy,

00:03:13.790 --> 00:03:16.100
and we are our maximum kinetic energy

00:03:16.100 --> 00:03:19.180
when the box crosses position zero.

00:03:19.180 --> 00:03:21.630
Well, the first time it
crosses position zero

00:03:21.630 --> 00:03:23.780
is at time equals one second.

00:03:23.780 --> 00:03:27.460
So we have our maximum kinetic
energy right over there.

00:03:27.460 --> 00:03:31.320
And then when we get to time equals two,

00:03:31.320 --> 00:03:33.400
our box is at position negative A.

00:03:33.400 --> 00:03:36.380
We no longer, for a moment,
we won't have any velocity,

00:03:36.380 --> 00:03:38.020
and our kinetic energy is gone.

00:03:38.020 --> 00:03:40.120
And so you can see how this is going.

00:03:40.120 --> 00:03:44.450
We keep switching between
potential and kinetic energy

00:03:44.450 --> 00:03:49.450
as the box keeps oscillating
between position A and

00:03:51.071 --> 00:03:53.200
position negative A.

00:03:53.200 --> 00:03:57.460
Once again, this is my
hand-drawn depiction of it.

00:03:57.460 --> 00:04:00.280
So that is our kinetic energy.

00:04:00.280 --> 00:04:02.670
Now, when we first introduced
ourselves to energy

00:04:02.670 --> 00:04:05.040
and the law of conservation of energy,

00:04:05.040 --> 00:04:08.960
we saw that, hey, look if
we are in a closed system

00:04:08.960 --> 00:04:10.940
and there are no dissipative forces

00:04:10.940 --> 00:04:12.300
and we're not adding energy

00:04:12.300 --> 00:04:15.820
or taking away energy
from that closed system

00:04:15.820 --> 00:04:18.550
and if we're just dealing with
mechanical energy and this,

00:04:18.550 --> 00:04:20.130
and non-dissipative forces,

00:04:20.130 --> 00:04:23.180
well, then mechanical
energy should be conserved.

00:04:23.180 --> 00:04:26.880
If we say that the total
mechanical energy of the system E

00:04:26.880 --> 00:04:29.760
is equal to our potential energy,

00:04:29.760 --> 00:04:32.720
which, in this case, is all
elastic potential energy,

00:04:32.720 --> 00:04:36.710
plus our kinetic energy,
this should be constant.

00:04:36.710 --> 00:04:38.420
And it is indeed the case.

00:04:38.420 --> 00:04:39.730
If, at any point in time,

00:04:39.730 --> 00:04:41.950
you were to add these two curves up,

00:04:41.950 --> 00:04:44.000
you would get something
that looks like this.

00:04:44.000 --> 00:04:45.800
It would just be a constant line,

00:04:45.800 --> 00:04:47.800
and that would be the graph

00:04:47.800 --> 00:04:51.610
of our mechanical potential energy.

00:04:51.610 --> 00:04:52.860
Now, an interesting question is,

00:04:52.860 --> 00:04:55.030
what if we did have dissipative forces?

00:04:55.030 --> 00:04:57.760
What would things look like then?

00:04:57.760 --> 00:04:59.690
Well, if we had dissipative forces,

00:04:59.690 --> 00:05:02.020
say friction or air resistance,

00:05:02.020 --> 00:05:03.990
well, then the box might
start at position A,

00:05:03.990 --> 00:05:06.000
but then it wouldn't get
all the way to negative A.

00:05:06.000 --> 00:05:07.550
It might look something like this.

00:05:07.550 --> 00:05:08.940
It might start here,

00:05:08.940 --> 00:05:11.290
but it might not get all
the way to negative A.

00:05:11.290 --> 00:05:15.320
And then it would get
even not as far this time,

00:05:15.320 --> 00:05:16.920
and then it would get,

00:05:16.920 --> 00:05:18.780
and I'm trying to draw
it as best as I can,

00:05:18.780 --> 00:05:21.290
and then it would get
even not as far that time.

00:05:21.290 --> 00:05:24.020
And if we think about
it in terms of energy,

00:05:24.020 --> 00:05:27.230
the total mechanical
energy would decrease.

00:05:27.230 --> 00:05:28.500
Where is it going?

00:05:28.500 --> 00:05:31.470
Well, it is being transformed
into thermal energy

00:05:31.470 --> 00:05:34.980
by the dissipative forces of
friction and air resistance.

00:05:34.980 --> 00:05:37.460
So the total energy would decrease,

00:05:37.460 --> 00:05:41.320
and then this would define the
envelope for the oscillations

00:05:41.320 --> 00:05:44.720
for the potential energy
and the kinetic energy.

00:05:44.720 --> 00:05:47.440
So, for example, the kinetic
energy in that situation

00:05:47.440 --> 00:05:49.200
would look like this.

00:05:49.200 --> 00:05:51.580
It would look like,

00:05:51.580 --> 00:05:53.460
it would look like this,

00:05:53.460 --> 00:05:57.000
where the peaks are going
to be bounded by this total,

00:05:57.000 --> 00:05:59.490
by this total mechanical energy.

00:05:59.490 --> 00:06:00.840
So I will leave you there.

00:06:00.840 --> 00:06:02.270
Hopefully this gives you a sense

00:06:02.270 --> 00:06:05.420
of how potential energy, kinetic energy,

00:06:05.420 --> 00:06:07.910
especially when you're dealing
with a spring-block system,

00:06:07.910 --> 00:06:09.520
how they relate to each other,

00:06:09.520 --> 00:06:12.520
especially in relation to the
law of conservation of energy.


Gravitational potential energy at large distances

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:00.983
- [Tutor] Let's do a little bit

00:00:00.983 --> 00:00:03.170
of a review of potential energy

00:00:03.170 --> 00:00:05.257
and especially gravitational
potential energy,

00:00:05.257 --> 00:00:06.371
because in this video,

00:00:06.371 --> 00:00:09.890
we're going to get a
little bit more precise.

00:00:09.890 --> 00:00:12.100
So let's say that I have an object here,

00:00:12.100 --> 00:00:14.320
it has a mass of M

00:00:14.320 --> 00:00:16.547
and I were to change its position
in the vertical direction,

00:00:16.547 --> 00:00:18.423
we're assuming that we are on Earth,

00:00:18.423 --> 00:00:20.850
where the gravitational field is G

00:00:20.850 --> 00:00:25.350
and we have a change in the
vertical direction of delta y,

00:00:25.350 --> 00:00:30.350
so this is its new position,
the object of mass, M,

00:00:31.120 --> 00:00:34.740
so what is its change in
gravitational potential energy?

00:00:34.740 --> 00:00:36.520
Well, we have seen this before,

00:00:36.520 --> 00:00:40.030
our change in potential
energy, due to gravity

00:00:40.030 --> 00:00:42.570
is going to be the mass of our object

00:00:42.570 --> 00:00:44.800
times the gravitational field

00:00:44.800 --> 00:00:49.800
times our change in position
in the vertical direction.

00:00:49.963 --> 00:00:52.474
Now this is all good, but
there's a couple of things,

00:00:52.474 --> 00:00:54.102
that we can get a little bit more precise,

00:00:54.102 --> 00:00:56.410
that we can think about in this video,

00:00:56.410 --> 00:00:58.703
one is we assumed a
constant gravitational field

00:00:58.703 --> 00:01:02.020
and that's fine if we're
near the surface of a planet

00:01:02.020 --> 00:01:05.487
and we also are just doing
everything on a relative basis,

00:01:05.487 --> 00:01:09.210
but is there a way to come
up with an absolute number

00:01:09.210 --> 00:01:13.100
on what is the gravitational
potential energy?

00:01:13.100 --> 00:01:14.960
Well, to think about that,

00:01:14.960 --> 00:01:17.950
let's just go back to
Newton's Law of Gravity,

00:01:17.950 --> 00:01:20.910
Newton's Law of Gravity tells
us that if I have two objects,

00:01:20.910 --> 00:01:23.610
so this object has mass, M1,

00:01:23.610 --> 00:01:25.313
this object has mass, M2

00:01:26.410 --> 00:01:29.643
and the distance between
their center of masses is r,

00:01:30.580 --> 00:01:34.890
that the magnitude of the force of gravity

00:01:34.890 --> 00:01:36.770
and if the force of gravity's

00:01:36.770 --> 00:01:38.295
acting in this direction on that object,

00:01:38.295 --> 00:01:40.560
it would have an equal
and opposite direction

00:01:40.560 --> 00:01:43.170
on that object right over there,

00:01:43.170 --> 00:01:45.070
so the magnitude of the force of gravity

00:01:45.070 --> 00:01:47.370
is going to be equal to
the gravitational constant

00:01:47.370 --> 00:01:50.310
times the product of
the two objects' masses

00:01:50.310 --> 00:01:53.490
divided by the radius squared

00:01:53.490 --> 00:01:54.540
or another way to think about it,

00:01:54.540 --> 00:01:58.710
if we wanna know the
gravitational field created by M2,

00:01:58.710 --> 00:02:00.902
well then you would just
divide both sides by M1,

00:02:00.902 --> 00:02:03.970
so if you divide both sides by M1,

00:02:03.970 --> 00:02:05.740
you get that the gravitational field

00:02:05.740 --> 00:02:07.360
actually isn't constant,

00:02:07.360 --> 00:02:10.520
it is equal to the gravitational constant

00:02:10.520 --> 00:02:14.420
times, these cancel out, M2,

00:02:14.420 --> 00:02:17.830
the mass of the object generating
the gravitational field

00:02:17.830 --> 00:02:20.590
divided by r squared

00:02:20.590 --> 00:02:22.024
and so this can actually help us

00:02:22.024 --> 00:02:24.360
come up with an absolute formula

00:02:24.360 --> 00:02:26.640
for gravitational potential energy.

00:02:26.640 --> 00:02:28.668
We can say that gravitational
potential energy

00:02:28.668 --> 00:02:32.400
and this is typically denoted
with a capital G over here

00:02:32.400 --> 00:02:35.648
is equal to, let's say
the mass of the object

00:02:35.648 --> 00:02:37.883
and let's just call that M1,

00:02:38.820 --> 00:02:40.370
the mass of the object

00:02:40.370 --> 00:02:43.870
times the gravitational field,

00:02:43.870 --> 00:02:48.330
so that's G times the mass of
the object creating the field

00:02:48.330 --> 00:02:50.030
divided by r squared

00:02:51.226 --> 00:02:52.830
times the height that this is

00:02:52.830 --> 00:02:56.380
above the center of mass of the object

00:02:56.380 --> 00:02:58.500
generating the gravitational field,

00:02:58.500 --> 00:02:59.522
well, what's that?

00:02:59.522 --> 00:03:03.040
Well, if this was Earth,
you would view r as,

00:03:03.040 --> 00:03:08.000
well, how far am I above
the center of mass of Earth?

00:03:08.000 --> 00:03:12.580
And so you would multiply that times r,

00:03:12.580 --> 00:03:14.310
times r

00:03:14.310 --> 00:03:17.098
and so this r and one of
the rs in the r squared

00:03:17.098 --> 00:03:19.123
will cancel out, so that will just go away

00:03:19.123 --> 00:03:21.690
and then this will just become an r

00:03:21.690 --> 00:03:23.220
and now one thing to think about

00:03:23.220 --> 00:03:25.980
is what should the potential energy be

00:03:25.980 --> 00:03:27.550
as r goes to infinity?

00:03:27.550 --> 00:03:31.450
Well, what is the gravitational
field as we go to infinity,

00:03:31.450 --> 00:03:33.890
as r gets really, really, really large?

00:03:33.890 --> 00:03:35.980
Well, as r gets really,
really, really large,

00:03:35.980 --> 00:03:39.262
the gravitational field goes to zero,

00:03:39.262 --> 00:03:41.940
but at the same time,
the further you get away,

00:03:41.940 --> 00:03:44.800
the higher the potential
energy you should have

00:03:44.800 --> 00:03:47.200
and so the way that
we've thought about this

00:03:47.200 --> 00:03:49.436
is we say, hey look, let's
just put a negative out front,

00:03:49.436 --> 00:03:51.800
you could just put it right over here

00:03:51.800 --> 00:03:53.897
and then it all works out,

00:03:53.897 --> 00:03:56.120
the gravitational potential energies

00:03:56.120 --> 00:03:57.479
are always gonna be negative,

00:03:57.479 --> 00:04:00.850
but they get less negative,
the further out you get to

00:04:00.850 --> 00:04:02.890
and at infinity, it gets to zero.

00:04:02.890 --> 00:04:04.263
So let me rewrite this.

00:04:04.263 --> 00:04:06.540
The potential energy, due to gravity

00:04:06.540 --> 00:04:11.540
can be written as the negative
of the gravitational constant

00:04:11.550 --> 00:04:13.263
times the mass of the first object

00:04:13.263 --> 00:04:17.160
time the mass of the
second object divided by r

00:04:17.160 --> 00:04:18.922
and you can see this looks an awful lot

00:04:18.922 --> 00:04:21.560
like Newton's Law of Gravity,

00:04:21.560 --> 00:04:22.740
what the difference is,

00:04:22.740 --> 00:04:25.620
we have a negative in front
of the gravitational constant,

00:04:25.620 --> 00:04:29.410
instead of dividing by r
squared, we only divide by r,

00:04:29.410 --> 00:04:32.380
but this is really, really,
really valuable now,

00:04:32.380 --> 00:04:34.817
because now we have an absolute sense

00:04:34.817 --> 00:04:37.230
of what gravitational potential energy is

00:04:37.230 --> 00:04:39.563
and it meets all the properties we need,

00:04:39.563 --> 00:04:44.040
it would still meet this idea
that the further you get away,

00:04:44.040 --> 00:04:48.100
you will have an increase in
gravitational potential energy,

00:04:48.100 --> 00:04:50.932
because it's going to
become less negative,

00:04:50.932 --> 00:04:53.570
but at the same time
as you go to infinity,

00:04:53.570 --> 00:04:55.750
as r gets infinitely far,

00:04:55.750 --> 00:04:59.770
your potential energy is
going to approach zero.

00:04:59.770 --> 00:05:00.990
So I will leave you there,

00:05:00.990 --> 00:05:03.423
in future videos, we will apply this.


Conservation of angular momentum

WEBVTT
Kind: captions
Language: en

00:00:00.238 --> 00:00:01.232
- [Instructor] Let's
talk a little bit about

00:00:01.232 --> 00:00:04.634
the conservation of angular momentum.

00:00:04.634 --> 00:00:06.506
And this is going to be really useful,

00:00:06.506 --> 00:00:10.005
because it explains diverse
phenomena in the universe.

00:00:10.005 --> 00:00:14.271
From why an ice skater's
angular speed goes up

00:00:14.271 --> 00:00:18.573
when they tuck their arms or
their legs in, all the way to

00:00:18.573 --> 00:00:22.115
when you have something
orbiting around a star,

00:00:22.115 --> 00:00:24.446
and the closer and closer it spirals in,

00:00:24.446 --> 00:00:27.830
it seems like its rotational
velocity's angular speed

00:00:27.830 --> 00:00:29.107
is picking up.

00:00:29.107 --> 00:00:31.762
And it starts to rotate faster
and faster around the body.

00:00:31.762 --> 00:00:33.242
You'll see that if you see simulations

00:00:33.242 --> 00:00:35.409
of astronomical phenomena.

00:00:36.439 --> 00:00:37.878
So the big picture here is,

00:00:37.878 --> 00:00:41.761
is if we have our initial angular momentum

00:00:41.761 --> 00:00:45.827
for a system, and we'll think
about that a little bit.

00:00:45.827 --> 00:00:50.311
As long as the system has no
external torque applied to it,

00:00:50.311 --> 00:00:54.037
then your final angular
momentum is going to be

00:00:54.037 --> 00:00:55.787
the exact same thing.

00:00:57.119 --> 00:00:59.215
And so, one way to think about it,

00:00:59.215 --> 00:01:01.788
let's imagine that I have some type of

00:01:01.788 --> 00:01:04.174
spinning thing over here.

00:01:04.174 --> 00:01:06.648
I have some type of mass,
let's say it's on a table,

00:01:06.648 --> 00:01:09.644
I'm looking from above, and a point on

00:01:09.644 --> 00:01:13.290
the outside of this disk is
spinning in this direction,

00:01:13.290 --> 00:01:15.873
with a velocity of magnitude v.

00:01:16.839 --> 00:01:20.717
And let's say that there's a
clump of clay, of orange...

00:01:20.717 --> 00:01:23.318
Maybe it's Play Doh, or clay or something.

00:01:23.318 --> 00:01:26.929
And it has a velocity
going in this direction.

00:01:26.929 --> 00:01:29.574
It's on a collision
course with this object.

00:01:29.574 --> 00:01:32.741
And let's say it has a velocity of 5v.

00:01:33.912 --> 00:01:38.912
And so, if we think about
this disk-clay clump system,

00:01:39.185 --> 00:01:40.850
and so you always have
to specify what system

00:01:40.850 --> 00:01:42.631
you are talking about,

00:01:42.631 --> 00:01:45.438
so if you think about this entire system,

00:01:45.438 --> 00:01:49.092
how does the angular momentum change

00:01:49.092 --> 00:01:51.331
before these two things collide,

00:01:51.331 --> 00:01:53.341
and then after these two things collide?

00:01:53.341 --> 00:01:55.822
So actually, let me draw the
after the collision scenario.

00:01:55.822 --> 00:01:57.565
So the after the collision scenario,

00:01:57.565 --> 00:01:59.275
it looks something like this,

00:01:59.275 --> 00:02:02.973
where the clay has now clumped onto this,

00:02:02.973 --> 00:02:06.115
and now they are going
to be rotating together.

00:02:06.115 --> 00:02:08.454
And I haven't even told
you the mass of this disk,

00:02:08.454 --> 00:02:10.264
or the mass of this clay,

00:02:10.264 --> 00:02:12.923
so it would be unclear in which direction

00:02:12.923 --> 00:02:15.318
they would now be rotating.

00:02:15.318 --> 00:02:17.857
But how is the angular
momentum going to change

00:02:17.857 --> 00:02:20.540
from this state, from the initial state,

00:02:20.540 --> 00:02:22.123
to the final state?

00:02:23.621 --> 00:02:26.140
Pause this video and
try to think about it.

00:02:26.140 --> 00:02:27.687
Well, you might have guessed.

00:02:27.687 --> 00:02:30.100
Since we said, look, we
have this whole system,

00:02:30.100 --> 00:02:34.264
and we're not applying any
external torque to the system,

00:02:34.264 --> 00:02:38.820
our angular momentum is going
to stay exactly the same.

00:02:38.820 --> 00:02:40.150
Now, we have to be careful.

00:02:40.150 --> 00:02:44.506
If I told you the system
was just this disk,

00:02:44.506 --> 00:02:48.590
not the clay clump that's on
a collision course with it,

00:02:48.590 --> 00:02:52.497
then the angular momentum
for the disk would change,

00:02:52.497 --> 00:02:53.891
but why is that?

00:02:53.891 --> 00:02:56.483
Does that defy the conservation
of angular momentum?

00:02:56.483 --> 00:02:57.316
No.

00:02:57.316 --> 00:02:59.263
Because this clay clump, when it collides,

00:02:59.263 --> 00:03:02.620
would be providing an
external torque to the system,

00:03:02.620 --> 00:03:05.517
if we defined the system
to just be the disk.

00:03:05.517 --> 00:03:08.188
But since it's the disk
plus the clay clump,

00:03:08.188 --> 00:03:11.718
and we have no external torque
to that combined system,

00:03:11.718 --> 00:03:15.801
then our angular momentum
is not going to change.

00:03:16.766 --> 00:03:17.769
Now that we can appreciate

00:03:17.769 --> 00:03:19.613
that angular momentum is constant

00:03:19.613 --> 00:03:22.365
as long as that there is no net torque

00:03:22.365 --> 00:03:24.776
applied to the system,

00:03:24.776 --> 00:03:28.242
let's think about the famous
situation where an ice skater's

00:03:28.242 --> 00:03:32.326
angular speed goes up as
they tuck in their arms.

00:03:32.326 --> 00:03:34.583
And you can do a less
graceful version of this

00:03:34.583 --> 00:03:35.888
on an office chair,

00:03:35.888 --> 00:03:39.875
where if you sit on the office
chair and you begin spinning,

00:03:39.875 --> 00:03:43.223
this is my office chair, and
if you stick your legs out,

00:03:43.223 --> 00:03:45.152
at first you're going to spin slowly,

00:03:45.152 --> 00:03:46.501
but then if you tuck your legs in,

00:03:46.501 --> 00:03:48.309
you're gonna start spinning faster.

00:03:48.309 --> 00:03:51.108
You're gonna have a higher angular speed.

00:03:51.108 --> 00:03:52.688
Now, why is that?

00:03:52.688 --> 00:03:54.842
Well, to appreciate
that, we can think about

00:03:54.842 --> 00:03:57.898
the formula for angular momentum.

00:03:57.898 --> 00:04:00.926
So the formula for angular momentum, L,

00:04:00.926 --> 00:04:02.256
there's a couple of ways we can,

00:04:02.256 --> 00:04:04.209
or several ways that we can write that.

00:04:04.209 --> 00:04:08.700
We can write that as our
moment of inertia, I,

00:04:08.700 --> 00:04:10.700
times our angular speed.

00:04:11.819 --> 00:04:12.819
Times omega.

00:04:14.134 --> 00:04:16.498
And this might look a little
bit foreign at first to you,

00:04:16.498 --> 00:04:18.697
but it has a complete analog

00:04:18.697 --> 00:04:20.496
when we're dealing in the linear world.

00:04:20.496 --> 00:04:21.620
Here we're rotating.

00:04:21.620 --> 00:04:25.822
In the linear world, we
say that linear momentum

00:04:25.822 --> 00:04:27.239
is equal to mass,

00:04:28.347 --> 00:04:31.014
is equal to mass times velocity.

00:04:32.885 --> 00:04:34.752
And the reason why we have an analog here,

00:04:34.752 --> 00:04:38.511
is mass can tell you about
inertia of an object.

00:04:38.511 --> 00:04:40.503
How much force do you need to apply

00:04:40.503 --> 00:04:42.479
to accelerate that object?

00:04:42.479 --> 00:04:43.775
f equals ma.

00:04:43.775 --> 00:04:45.022
Well, moment of inertia,

00:04:45.022 --> 00:04:46.782
you have something similar going on.

00:04:46.782 --> 00:04:47.615
But instead of thinking

00:04:47.615 --> 00:04:50.101
about how to just linearly
accelerate something,

00:04:50.101 --> 00:04:53.682
this tells you how hard is it
to get angular acceleration,

00:04:53.682 --> 00:04:56.157
how much torque do you need to apply?

00:04:56.157 --> 00:04:57.750
Instead of just how much linear force

00:04:57.750 --> 00:04:58.849
you need to apply.

00:04:58.849 --> 00:05:01.494
And instead of velocity,
you have angular speed,

00:05:01.494 --> 00:05:04.344
and sometimes this is called
angular velocity as well.

00:05:04.344 --> 00:05:05.345
But this by itself, you might say,

00:05:05.345 --> 00:05:08.061
well this doesn't help
me on tucking in my knees

00:05:08.061 --> 00:05:09.565
when I'm on an office chair,

00:05:09.565 --> 00:05:12.031
or the ice skater tucking in her arms.

00:05:12.031 --> 00:05:14.675
Well, to think about that,
we just have to appreciate

00:05:14.675 --> 00:05:18.866
that the moment of inertia
can be expressed as

00:05:18.866 --> 00:05:21.866
m times radius squared, m r squared.

00:05:23.441 --> 00:05:26.974
And then we still have
our omega right over here.

00:05:26.974 --> 00:05:31.058
So this is another way of
writing angular momentum.

00:05:31.058 --> 00:05:35.083
And so, when a skater tucks in her arms,

00:05:35.083 --> 00:05:38.270
her mass is not changing,
that is staying constant.

00:05:38.270 --> 00:05:40.633
But remember, the radius,
one way to think about it,

00:05:40.633 --> 00:05:42.037
it's a little complicated
when you're thinking about

00:05:42.037 --> 00:05:43.634
a human body system.

00:05:43.634 --> 00:05:47.000
In a simple sense you
just have a point mass

00:05:47.000 --> 00:05:49.341
rotating around a point like that,

00:05:49.341 --> 00:05:51.102
then this is the radius.

00:05:51.102 --> 00:05:53.775
But if we're dealing with a
more complicated structure,

00:05:53.775 --> 00:05:54.917
like a human body,

00:05:54.917 --> 00:05:57.862
you can imagine the
radius as being indicative

00:05:57.862 --> 00:06:01.270
of the average distance of the mass,

00:06:01.270 --> 00:06:03.700
from the center of rotation.

00:06:03.700 --> 00:06:06.633
So when the figure
skater tucks in her arms,

00:06:06.633 --> 00:06:08.660
that average distance goes down.

00:06:08.660 --> 00:06:11.988
And so when she tucks in
her arm, this goes down,

00:06:11.988 --> 00:06:15.099
but if this part goes down,
but our angular momentum

00:06:15.099 --> 00:06:17.964
stays constant, because we have no torque

00:06:17.964 --> 00:06:19.240
being applied to the system,

00:06:19.240 --> 00:06:20.949
no net torque being applied to the system,

00:06:20.949 --> 00:06:23.947
well then, this needs to
go up in order to keep

00:06:23.947 --> 00:06:26.215
that angular momentum constant.

00:06:26.215 --> 00:06:27.978
And that's exactly what's happening.

00:06:27.978 --> 00:06:32.728
The angular speed picks up,
just as the radius goes down.

00:06:34.475 --> 00:06:38.226
Now, this also explains why if you have,

00:06:38.226 --> 00:06:41.098
let's say that's some type of planet,

00:06:41.098 --> 00:06:44.715
and you have a rock, or
something orbiting it.

00:06:44.715 --> 00:06:48.545
As this gets closer and
closer to the planet,

00:06:48.545 --> 00:06:50.920
it's angular speed is going to go higher,

00:06:50.920 --> 00:06:52.358
and higher, and higher.

00:06:52.358 --> 00:06:53.438
Why is that?

00:06:53.438 --> 00:06:55.445
Well, because when you have a high radius,

00:06:55.445 --> 00:06:57.613
so here your radius is higher,

00:06:57.613 --> 00:07:00.826
and so your angular speed
might be a little bit lower,

00:07:00.826 --> 00:07:05.826
but then when you're closer
in, your radius has gone down.

00:07:05.937 --> 00:07:10.687
And so your angular speed has
to go up to make up for it.

00:07:11.942 --> 00:07:13.332
I'll leave you there.

00:07:13.332 --> 00:07:16.229
I encourage you to have fun
spinning on office chairs.


Conclusion for a two-sample t test using a confidence interval

WEBVTT
Kind: captions
Language: en

00:00:00.000 --> 00:00:03.030
- [Voiceover] Yuna grows
two varieties of pears,

00:00:03.030 --> 00:00:04.750
Bosc and Anjou.

00:00:04.750 --> 00:00:07.210
She took a sample of each variety to test

00:00:07.210 --> 00:00:09.160
if their average caloric contents

00:00:09.160 --> 00:00:10.700
were significantly different.

00:00:10.700 --> 00:00:14.910
Here is a summary of her results.

00:00:14.910 --> 00:00:19.150
And so they give the same data
for both of these samples,

00:00:19.150 --> 00:00:21.040
and once again they happen
to have the sample size,

00:00:21.040 --> 00:00:22.440
they don't need to.

00:00:22.440 --> 00:00:25.700
But over here instead
of giving us a P-value,

00:00:25.700 --> 00:00:28.240
we've gotten a confidence interval.

00:00:28.240 --> 00:00:31.950
Yuna wants to use these results
to test her null hypothesis

00:00:31.950 --> 00:00:35.220
that the mean caloric content is the same,

00:00:35.220 --> 00:00:37.200
versus her alternative hypothesis,

00:00:37.200 --> 00:00:39.030
that they are different.

00:00:39.030 --> 00:00:42.170
Assume that all conditions
for inference have been met.

00:00:42.170 --> 00:00:44.850
Based on the interval, what do we know

00:00:44.850 --> 00:00:46.850
about the corresponding P-value

00:00:46.850 --> 00:00:49.570
and conclusion at the alpha is equal

00:00:49.570 --> 00:00:52.850
to 0.01 level of significance?

00:00:52.850 --> 00:00:55.653
So pause this video and see
if you can figure that out.

00:00:56.800 --> 00:01:00.663
Remember what a 99%
confidence interval is.

00:01:00.663 --> 00:01:04.833
That says that if we
construct confidence intervals

00:01:04.833 --> 00:01:09.833
100 times, that 99 of those
times we should overlap

00:01:10.045 --> 00:01:14.370
with the true parameter that
we're trying to estimate.

00:01:14.370 --> 00:01:16.220
In that case the true parameter

00:01:16.220 --> 00:01:19.630
is the true difference of these means.

00:01:19.630 --> 00:01:21.980
Now when we do a hypothesis test,

00:01:21.980 --> 00:01:25.770
we always start assuming that
the null hypothesis is true.

00:01:25.770 --> 00:01:29.850
And so if we assume that
the null hypothesis is true,

00:01:29.850 --> 00:01:32.830
well another way of writing
this null hypothesis,

00:01:32.830 --> 00:01:34.060
if the two means are equal,

00:01:34.060 --> 00:01:35.160
that's the same thing as

00:01:35.160 --> 00:01:38.560
the difference of the means equaling zero.

00:01:38.560 --> 00:01:40.470
And since we're assuming this,

00:01:40.470 --> 00:01:43.146
and this a 99% confidence interval,

00:01:43.146 --> 00:01:47.040
then 99 out of 100 times that we do this,

00:01:47.040 --> 00:01:50.010
we should see that this interval overlaps

00:01:50.010 --> 00:01:53.140
with what we're assuming
is the true parameter

00:01:53.140 --> 00:01:54.810
right over here.

00:01:54.810 --> 00:01:58.890
Now this interval does
indeed overlap with zero,

00:01:58.890 --> 00:02:01.040
if you take four minus 6.44,

00:02:01.040 --> 00:02:03.200
you're gonna get negative 2.44.

00:02:03.200 --> 00:02:05.860
So zero is definitely in the interval.

00:02:05.860 --> 00:02:07.190
And so another way to think about it,

00:02:07.190 --> 00:02:09.700
we're not in the 1% of the times

00:02:09.700 --> 00:02:11.210
where we don't overlap.

00:02:11.210 --> 00:02:14.600
If we were in the 1% of
times where we don't overlap

00:02:14.600 --> 00:02:17.630
with the assumed difference,

00:02:17.630 --> 00:02:20.990
then we would reject the null hypothesis.

00:02:20.990 --> 00:02:23.260
Or another way to think about it is

00:02:23.260 --> 00:02:26.870
our significance level
0.01 right over here,

00:02:26.870 --> 00:02:31.440
it's one minus our confidence
level, right over here.

00:02:31.440 --> 00:02:35.950
If our 99% confidence interval overlaps

00:02:38.900 --> 00:02:43.900
with mu from the Bosc pears

00:02:45.200 --> 00:02:48.170
minus the mean caloric content

00:02:48.170 --> 00:02:51.860
of the Anjou pears, equaling zero,

00:02:51.860 --> 00:02:53.520
then that means,

00:02:53.520 --> 00:02:55.830
that means that the P-value

00:02:55.830 --> 00:02:59.190
is greater than 0.01.

00:02:59.190 --> 00:03:01.580
And so we could also
say that our p-value is

00:03:01.580 --> 00:03:02.940
greater than our significance level,

00:03:02.940 --> 00:03:04.750
because that is our significance level,

00:03:04.750 --> 00:03:09.750
and because of that we fail
to reject our null hypothesis.

00:03:12.890 --> 00:03:15.340
If this did not overlap

00:03:15.340 --> 00:03:17.750
with our assumed difference in the means,

00:03:17.750 --> 00:03:20.070
if it did not overlap with zero,

00:03:20.070 --> 00:03:23.080
then we would be in that
one in a hundred scenario

00:03:23.080 --> 00:03:26.130
and then that would tell
us that hey our p-value

00:03:26.130 --> 00:03:28.630
is less than 0.01.

00:03:28.630 --> 00:03:32.390
Our P-value is less than one
minus our confidence level

00:03:32.390 --> 00:03:35.510
and in that case we would
reject the null hypothesis

00:03:35.510 --> 00:03:36.690
and it would suggest that

00:03:36.690 --> 00:03:39.820
there is a difference in caloric content.

00:03:39.820 --> 00:03:41.390
But because we failed to reject it,

00:03:41.390 --> 00:03:42.670
we can't conclude that

00:03:42.670 --> 00:03:45.013
there's a difference in caloric content.


Conclusion for a two-sample t test using a P-value

WEBVTT
Kind: captions
Language: en

00:00:00.140 --> 00:00:02.030
- [Instructor] A sociologist
studying fertility

00:00:02.030 --> 00:00:04.480
in France and Switzerland wanted to test

00:00:04.480 --> 00:00:07.390
if there was a difference in
the average number of babies

00:00:07.390 --> 00:00:09.570
women in each country have.

00:00:09.570 --> 00:00:12.680
The sociologist obtained
a random sample of women

00:00:12.680 --> 00:00:13.800
from each country.

00:00:13.800 --> 00:00:16.520
Here are the results of their test.

00:00:16.520 --> 00:00:20.010
So you can see a 100-person
sample from France,

00:00:20.010 --> 00:00:21.660
a 100-person sample from Switzerland.

00:00:21.660 --> 00:00:23.840
They actually don't have
to be the same sample size.

00:00:23.840 --> 00:00:26.980
We have our sample means, our
sample standard deviations.

00:00:26.980 --> 00:00:29.160
You have the standard error of the mean,

00:00:29.160 --> 00:00:31.780
which for each sample
would be our estimate

00:00:31.780 --> 00:00:35.466
of the standard deviation
of the sampling distribution

00:00:35.466 --> 00:00:37.780
of the sample mean.

00:00:37.780 --> 00:00:40.272
And here it says t test for the means

00:00:40.272 --> 00:00:43.010
of these different
populations being different.

00:00:43.010 --> 00:00:44.890
And just to make sure we
can make sense of this,

00:00:44.890 --> 00:00:47.090
let's just remind
ourselves what's going on.

00:00:47.090 --> 00:00:49.640
The null hypothesis is
that there's no difference

00:00:49.640 --> 00:00:53.206
in the mean number of babies
that women in France have

00:00:53.206 --> 00:00:56.090
versus the mean number of babies

00:00:56.090 --> 00:00:57.240
that women in Switzerland have.

00:00:57.240 --> 00:00:58.560
That would be our null hypothesis,

00:00:58.560 --> 00:01:00.150
the no news here hypothesis.

00:01:00.150 --> 00:01:02.620
And our alternative would
be that they are different.

00:01:02.620 --> 00:01:04.260
And that's what we have right over here.

00:01:04.260 --> 00:01:06.110
It's a t test to see if we have evidence

00:01:06.110 --> 00:01:09.330
that would suggest our
alternative hypothesis.

00:01:09.330 --> 00:01:12.450
And so what we do is we
assume the null hypothesis.

00:01:12.450 --> 00:01:15.660
From that you're able to
calculate a t-statistic,

00:01:15.660 --> 00:01:19.730
and then from that t-statistic
and the degrees of freedom,

00:01:19.730 --> 00:01:22.680
you are able to calculate a p-value.

00:01:22.680 --> 00:01:27.050
And if that p-value is below
your significance level,

00:01:27.050 --> 00:01:29.320
then you'd say hey this was
pretty unlikely scenario,

00:01:29.320 --> 00:01:31.370
let me reject the null hypothesis,

00:01:31.370 --> 00:01:34.140
which would suggest the alternative.

00:01:34.140 --> 00:01:37.590
But if your p-value is greater
than your significance level,

00:01:37.590 --> 00:01:40.250
then you would fail to
reject your null hypothesis,

00:01:40.250 --> 00:01:42.770
and so you would not
have sufficient evidence

00:01:42.770 --> 00:01:45.260
to conclude the alternative.

00:01:45.260 --> 00:01:46.610
So what's going on over here?

00:01:46.610 --> 00:01:48.725
You really just have to compare this value

00:01:48.725 --> 00:01:50.140
to this value.

00:01:50.140 --> 00:01:53.508
It says at the alpha is equal
to 0.05 level of significance,

00:01:53.508 --> 00:01:55.720
is there sufficient evidence to conclude

00:01:55.720 --> 00:01:58.350
that there is a difference in
the average number of babies

00:01:58.350 --> 00:02:00.940
women in each country have?

00:02:00.940 --> 00:02:05.280
Well we can see that our p-value, 0.13,

00:02:05.280 --> 00:02:09.400
is greater than our alpha value, 0.05.

00:02:09.400 --> 00:02:11.030
And so because of that,

00:02:11.030 --> 00:02:15.220
we fail to reject

00:02:15.220 --> 00:02:16.690
our null hypothesis.

00:02:16.690 --> 00:02:18.120
And to answer their question,

00:02:18.120 --> 00:02:20.510
no there is not sufficient evidence

00:02:20.510 --> 00:02:22.730
to conclude that there is a difference.

00:02:22.730 --> 00:02:24.800
There's not sufficient evidence to reject

00:02:24.800 --> 00:02:28.053
the null hypothesis and
suggest the alternative.


Two-sample t test for difference of means

WEBVTT
Kind: captions
Language: en

00:00:00.167 --> 00:00:03.667
- [Instructor] "Kaito grows
tomatoes in two separate fields.

00:00:03.667 --> 00:00:05.837
"When the tomatoes are ready to be picked,

00:00:05.837 --> 00:00:09.577
"he is curious as to whether
the sizes of his tomato plants

00:00:09.577 --> 00:00:11.957
"differ between the two fields.

00:00:11.957 --> 00:00:15.517
"He takes a random sample
of plants from each field

00:00:15.517 --> 00:00:18.957
"and measures the heights of the plants.

00:00:18.957 --> 00:00:22.140
"Here is a summary of the results:"

00:00:22.140 --> 00:00:24.240
So what I want you to
do, is pause this video,

00:00:24.240 --> 00:00:28.070
and conduct a two sample T test here.

00:00:28.070 --> 00:00:30.580
And let's assume that
all of the conditions

00:00:30.580 --> 00:00:33.870
for inference are met,
the random condition,

00:00:33.870 --> 00:00:37.090
the normal condition, and
the independent condition.

00:00:37.090 --> 00:00:38.670
And let's assume that we are working

00:00:38.670 --> 00:00:42.150
with a significance level of 0.05.

00:00:42.150 --> 00:00:46.650
So pause the video, and conduct
the two sample T test here,

00:00:46.650 --> 00:00:47.910
to see whether there's evidence

00:00:47.910 --> 00:00:52.220
that the sizes of tomato plants
differ between the fields.

00:00:52.220 --> 00:00:54.800
Alright, now let's work
through this together.

00:00:54.800 --> 00:00:58.770
So like always, let's first
construct our null hypothesis.

00:00:58.770 --> 00:01:00.980
And that's going to be the situation

00:01:00.980 --> 00:01:04.230
where there is no difference
between the mean sizes,

00:01:04.230 --> 00:01:07.300
so that would be that
the mean size in field A

00:01:07.300 --> 00:01:11.110
is equal to the mean size in field B.

00:01:11.110 --> 00:01:14.080
Now what about our alternative hypothesis?

00:01:14.080 --> 00:01:17.430
Well, he wants to see whether
the sizes of his tomato plants

00:01:17.430 --> 00:01:19.140
differ between the two fields.

00:01:19.140 --> 00:01:21.980
He's not saying whether
A is bigger than B,

00:01:21.980 --> 00:01:23.950
or whether B is bigger than A,

00:01:23.950 --> 00:01:26.060
and so his alternative hypothesis

00:01:26.060 --> 00:01:27.830
would be around his suspicion,

00:01:27.830 --> 00:01:32.810
that the mean of A is not
equal to the mean of B,

00:01:32.810 --> 00:01:34.370
that they differ.

00:01:34.370 --> 00:01:38.760
And to do this two sample T test now,

00:01:38.760 --> 00:01:42.210
we assume the null hypothesis.

00:01:42.210 --> 00:01:45.030
We assume our null hypothesis,

00:01:45.030 --> 00:01:46.160
and remember we're assuming that all

00:01:46.160 --> 00:01:47.940
of our conditions for inference are met.

00:01:47.940 --> 00:01:50.850
And then we wanna calculate a T statistic

00:01:50.850 --> 00:01:54.160
based on this sample data that we have.

00:01:54.160 --> 00:01:57.190
And our T statistic is going to be equal

00:01:57.190 --> 00:02:00.253
to the differences
between the sample means,

00:02:01.220 --> 00:02:03.550
all of that over our estimate

00:02:03.550 --> 00:02:06.370
of the standard deviation
of the sampling distribution

00:02:06.370 --> 00:02:08.920
of the difference of the sample means.

00:02:08.920 --> 00:02:11.500
This will be the sample standard deviation

00:02:11.500 --> 00:02:16.500
from sample A squared, over
the sample size from A,

00:02:16.900 --> 00:02:19.000
plus the sample standard deviation

00:02:19.000 --> 00:02:23.970
from the B sample squared,
over the sample size from B.

00:02:23.970 --> 00:02:25.940
And let's see, we have
all the numbers here

00:02:25.940 --> 00:02:27.250
to calculate it.

00:02:27.250 --> 00:02:32.250
This numerator is going to
be equal to 1.3 minus 1.6,

00:02:32.577 --> 00:02:36.580
1.3 minus 1.6, all of that over

00:02:36.580 --> 00:02:39.270
the square root of, let's see,

00:02:39.270 --> 00:02:42.060
the standard deviation, the
sample standard deviation

00:02:42.060 --> 00:02:44.790
from the sample from field A is 0.5.

00:02:44.790 --> 00:02:47.553
If you square that, you're gonna get 0.25,

00:02:49.950 --> 00:02:52.840
and then that's going to
be over the sample size

00:02:52.840 --> 00:02:56.250
from field A, over 22,

00:02:56.250 --> 00:03:00.050
plus 0.3 squared, so that is,

00:03:00.050 --> 00:03:05.050
0.3 squared is 0.09,

00:03:07.380 --> 00:03:10.770
all of that over the
sample size from field B,

00:03:10.770 --> 00:03:13.420
all of that over 24.

00:03:13.420 --> 00:03:15.227
The numerator is just gonna be -.3,

00:03:18.710 --> 00:03:22.140
divided by the square root

00:03:22.140 --> 00:03:27.140
of .25 divided by 22,

00:03:27.520 --> 00:03:32.520
plus .09 divided by 24,

00:03:33.820 --> 00:03:37.543
and that gets us -2.44.

00:03:39.720 --> 00:03:43.370
Approximately -2.44.

00:03:43.370 --> 00:03:46.810
And so if you think
about a T distribution,

00:03:46.810 --> 00:03:49.300
and we'll use our calculator
to figure out this probability,

00:03:49.300 --> 00:03:52.490
so this is a T distribution
right over here,

00:03:52.490 --> 00:03:57.080
this would be the assumed
mean of our T distribution.

00:03:57.080 --> 00:03:59.930
And so we got a result that is,

00:03:59.930 --> 00:04:02.540
we got a T statistic of -2.44,

00:04:02.540 --> 00:04:07.490
so we're right over
here, so this is -2.44.

00:04:07.490 --> 00:04:09.630
And so we wanna say
what is the probability

00:04:09.630 --> 00:04:12.230
from this T distribution
of getting something

00:04:12.230 --> 00:04:13.570
at least this extreme?

00:04:13.570 --> 00:04:18.570
So it would be this area, and
it would also be this area,

00:04:19.000 --> 00:04:22.890
if we got 2.44 above the mean,
it would also be this area.

00:04:22.890 --> 00:04:25.220
And so what I could do is,
I'm gonna use my calculator

00:04:25.220 --> 00:04:28.340
to figure out this
probability right over here,

00:04:28.340 --> 00:04:30.400
and then I'm just gonna
multiply that by two,

00:04:30.400 --> 00:04:32.350
to get this one as well.

00:04:32.350 --> 00:04:37.350
So the probability of getting a T value,

00:04:38.600 --> 00:04:41.580
I guess I could say
where its absolute value

00:04:41.580 --> 00:04:46.230
is greater than or equal to 2.44,

00:04:46.230 --> 00:04:49.960
is going to be approximately equal to,

00:04:49.960 --> 00:04:53.320
I'm going to go to second, distribution,

00:04:53.320 --> 00:04:56.410
I'm going to go to the
cumulative distribution function

00:04:56.410 --> 00:04:59.650
for our T distribution, click that.

00:04:59.650 --> 00:05:03.950
And since I wanna think about
this tail probability here

00:05:03.950 --> 00:05:05.160
that I'm just gonna multiply by two,

00:05:05.160 --> 00:05:08.370
the lower bound is a very
very very negative number,

00:05:08.370 --> 00:05:11.330
and you could view that as
functionally negative infinity.

00:05:11.330 --> 00:05:14.984
The upper bound is -2.44.

00:05:14.984 --> 00:05:16.573
- 2.44.

00:05:18.330 --> 00:05:20.980
And now what's our degrees of freedom?

00:05:20.980 --> 00:05:22.590
Well if we take the conservative approach,

00:05:22.590 --> 00:05:27.290
it'll be the smaller of
the two samples minus one.

00:05:27.290 --> 00:05:30.470
Well the smaller of the two samples is 22,

00:05:30.470 --> 00:05:33.193
and so 22 minus one is 21.

00:05:34.100 --> 00:05:36.420
So put 21 in there.

00:05:36.420 --> 00:05:37.752
Two...

00:05:37.752 --> 00:05:39.530
21.

00:05:39.530 --> 00:05:44.530
And now I can paste, and I get
that number right over there,

00:05:46.580 --> 00:05:48.970
and if I multiply that by
two, 'cause this just gives me

00:05:48.970 --> 00:05:51.300
the probability of getting
something lower than that,

00:05:51.300 --> 00:05:52.660
but I also wanna think
about the probability

00:05:52.660 --> 00:05:56.530
of getting something 2.44
or more above the mean

00:05:56.530 --> 00:05:57.870
of our T distribution.

00:05:57.870 --> 00:06:02.870
So times two, is going to be
equal to approximately 0.024.

00:06:07.240 --> 00:06:12.240
So approximately 0.024.

00:06:12.650 --> 00:06:14.870
And what I wanna do then is compare this

00:06:14.870 --> 00:06:16.400
to my significance level.

00:06:16.400 --> 00:06:19.540
And you can see very clearly,
this right over here,

00:06:19.540 --> 00:06:21.063
this is equal to our P value.

00:06:22.020 --> 00:06:24.210
Our P value in this situation,

00:06:24.210 --> 00:06:27.650
our P value in this
situation is clearly less

00:06:27.650 --> 00:06:29.290
than our significance level.

00:06:29.290 --> 00:06:31.480
And because of that, we said hey,

00:06:31.480 --> 00:06:33.320
assuming the null hypothesis is true,

00:06:33.320 --> 00:06:35.490
we got something that's
a pretty low probability

00:06:35.490 --> 00:06:38.110
below our threshold, so
we are going to reject

00:06:39.450 --> 00:06:42.980
our null hypothesis, which
tells us that there is,

00:06:42.980 --> 00:06:45.080
so this suggests,

00:06:45.080 --> 00:06:49.010
this suggests the alternative hypothesis,

00:06:49.010 --> 00:06:52.500
that there is indeed a
difference between the sizes

00:06:52.500 --> 00:06:55.203
of the tomato plants in the two fields.


Example of hypotheses for paired and two-sample t tests

WEBVTT
Kind: captions
Language: en

00:00:00.620 --> 00:00:02.690
- [Instructor] The Olympic
running team of Freedonia

00:00:02.690 --> 00:00:05.083
has always used Zeppo's running shoes,

00:00:05.083 --> 00:00:08.600
but their manager suspects
Harpo's shoes can produce

00:00:09.455 --> 00:00:11.030
better results, which
would be lower times.

00:00:11.030 --> 00:00:14.810
The manager has six
runners each run two laps.

00:00:14.810 --> 00:00:18.330
One lap wearing Zeppo's and
another lap wearing Harpo's.

00:00:18.330 --> 00:00:20.530
Each runner flips a coin to determine

00:00:20.530 --> 00:00:22.800
which shoes they wear first.

00:00:22.800 --> 00:00:25.350
The manager wants to test
if their times when wearing

00:00:25.350 --> 00:00:28.400
Harpo's are significantly
lower than their times

00:00:28.400 --> 00:00:30.180
when they wear Zeppo's.

00:00:30.180 --> 00:00:34.040
Assume that all conditions
for inference were met.

00:00:34.040 --> 00:00:36.810
Which of these is the
most appropriate test

00:00:36.810 --> 00:00:38.470
and alternative hypothesis?

00:00:38.470 --> 00:00:40.000
So they're just asking
this about the alternative

00:00:40.000 --> 00:00:42.840
not even the null but
we can talk about that.

00:00:42.840 --> 00:00:45.690
So pause this video and see
if you can figure it out.

00:00:45.690 --> 00:00:47.920
So before I even go into
this particular example

00:00:47.920 --> 00:00:49.640
let's just make sure we
understand the difference

00:00:49.640 --> 00:00:54.090
between a two-sample T
test and a paired T test.

00:00:54.090 --> 00:00:58.790
So when were talking about
either a two-sample T test

00:00:58.790 --> 00:01:02.180
or a two-sample T,
interval for the difference

00:01:02.180 --> 00:01:03.930
between the mean, what we're doing

00:01:03.930 --> 00:01:06.907
is we're considering two populations.

00:01:06.907 --> 00:01:11.030
You take two independent
samples from those populations.

00:01:11.030 --> 00:01:12.680
And what you're trying to do is,

00:01:12.680 --> 00:01:15.580
is you get statistics off of these samples

00:01:15.580 --> 00:01:18.490
and you're trying to estimate
the difference between

00:01:18.490 --> 00:01:21.300
the means of these populations.

00:01:21.300 --> 00:01:24.360
So it might be the difference
of Mue one minus Mue two.

00:01:24.360 --> 00:01:25.450
That's what you're trying to figure out,

00:01:25.450 --> 00:01:28.280
Mue one minus Mue two.

00:01:28.280 --> 00:01:30.920
A paired situation is quite different.

00:01:30.920 --> 00:01:33.360
Even though they might
sound the same at first.

00:01:33.360 --> 00:01:36.970
Here we're looking at just one population

00:01:36.970 --> 00:01:38.940
and that's exactly what's happening

00:01:38.940 --> 00:01:41.190
in this situation right over here.

00:01:41.190 --> 00:01:44.350
We're trying to figure out
what is the mean difference

00:01:44.350 --> 00:01:47.710
between using Zeppo's and Harpo's shoes.

00:01:47.710 --> 00:01:51.300
So this is what we're trying
to get at, the mean difference.

00:01:51.300 --> 00:01:56.300
So we could just call that
Mue sub Zeppo's minus Harpo's.

00:01:58.600 --> 00:02:00.470
And the way that we go about doing that

00:02:00.470 --> 00:02:04.440
is we take a sample and then
for each subject in the sample

00:02:04.440 --> 00:02:06.060
we perform two measurements.

00:02:06.060 --> 00:02:07.540
One where they run with the Zeppo's

00:02:07.540 --> 00:02:09.200
and one where they run with the Harpo's.

00:02:09.200 --> 00:02:14.200
And then for that sample you
can calculate a mean difference

00:02:14.250 --> 00:02:19.250
between the Zeppo's and the Harpo's.

00:02:19.410 --> 00:02:21.740
You're going to calculate
this difference for each

00:02:21.740 --> 00:02:23.990
member of your sample and
then you're going to take

00:02:23.990 --> 00:02:25.790
the mean of all of those.

00:02:25.790 --> 00:02:28.260
So hopefully you notice that
this is quite different.

00:02:28.260 --> 00:02:31.240
And so as you can imagine,
here in this example

00:02:31.240 --> 00:02:34.060
we are dealing with a paired T test.

00:02:34.060 --> 00:02:36.730
We aren't looking at
two independent groups

00:02:36.730 --> 00:02:39.020
or two independent samples like you would

00:02:39.020 --> 00:02:40.890
with the two-sample T test.

00:02:40.890 --> 00:02:43.350
And so we run a paired T test

00:02:43.350 --> 00:02:46.360
and the manager wants to test
if their times when wearing

00:02:46.360 --> 00:02:49.560
Harpo's are significantly lower than

00:02:49.560 --> 00:02:52.350
their times when wearing Zeppo's.

00:02:52.350 --> 00:02:55.200
So our null hypothesis, even
though that their not asking

00:02:56.084 --> 00:02:57.680
that, our null hypothesis would be

00:02:57.680 --> 00:02:59.100
that there's no difference.

00:02:59.100 --> 00:03:03.747
That the mean time, that
the mean difference between

00:03:05.440 --> 00:03:10.440
wearing Zeppo's, Zeppo's
and Harpo's, and Harpo's

00:03:12.180 --> 00:03:15.350
would be equal to zero.

00:03:15.350 --> 00:03:17.353
And the alternative hypothesis.

00:03:18.200 --> 00:03:21.030
So if they were just saying,
"Hey, is there a difference?"

00:03:21.030 --> 00:03:23.770
Then we would say that this
would not be equal to zero,

00:03:23.770 --> 00:03:24.830
the alternative.

00:03:24.830 --> 00:03:27.800
But the manager explicitly
want's to see if Harpo's times

00:03:27.800 --> 00:03:30.290
are lower than Zeppo's times.

00:03:30.290 --> 00:03:32.690
So what we would want to see
is if the mean difference,

00:03:32.690 --> 00:03:37.690
so the mean difference of
Zeppo's, Zeppo's minus Harpo's.

00:03:38.878 --> 00:03:41.190
We're trying to find if
we can see if we can have

00:03:41.190 --> 00:03:44.863
evidence to suggest that this
is actually greater than zero.

00:03:45.807 --> 00:03:48.433
And so that would be this
choice right over there.