1. Hypothesis Testing

A biologist discovers a colony of a previously unknown type of bird nesting in a cave. Out of the 16 chicks which hatch during his period of investigation, 13 are female. Test at the 5% significance level whether this supports the view that that the sex ratio for the chicks differs from 1.
Im really stuck i think ive developed the p:H1 and p:H0 but after that i am a bit stuck any help is much appreciated thankyou

2. Sounds like you should use a $\displaystyle \chi^2$ test here.

$\displaystyle H_0:$ Observed sex ratio can be described by the Expected sex ratio

$\displaystyle H_1:$ Observed sex ratio differs from the Expected sex ratio

Now you need to make a table

$\begin{array}{|c|c|c|}
& \text{Male} & \text{Female}\\ \hline
\text{Expected} & \dots & \dots \\ \text{Observed} & \dots & \dots \\ \chi^2_{calc} & \dots & \dots\\ \hline \end{array}$

Populate this table and find $\displaystyle \chi^2_{calc} = \Sum \frac{(\text{0bserved-Expected})^2}{\text{Expected}}$

If $\displaystyle \chi^2_{calc} > \chi^2_{crit}= \chi^2_{df,\alpha}$ reject $\displaystyle H_0$

3. I would test that the proportion of females is .5 versus not
Since n is small you cannot approximate with a normal and you will need to use the binomial distribution.
You can obtain the p-value with x=13
And n=16, p=.5.