All of the following are true about standard error ofmean except:
As the sample size increases, standard error will also increase Formula for standard error of mean is: S.E.= Standard detion /Vsample size Thus as the formula shows, the standard error is dependent on the size of the samples. Standard error is inversely related to the square root of the sample size, so that larger the sample size, the smaller will be the sampling error. This is reason why the results of larger studies or surveys are more trusted than the results of smaller ones. Standard error of mean If we take repeated samples from the same population or universe, the results obtained from one sample will differ to some extent from the results of another sample. This type of variation from one sample to another is called sampling error. It occurs because data were gathered from a sample rather from the entire population. If we take a random sample (1) from the population, and similar samples over and over again we will find that every sample will have a different mean( If we make a frequency distribution of all the sample means drawn from the same population, we will find that the distribution of the mean is nearly a normal distribution and the mean of the sample means practically the same as the population mean 44 The standard detion of the means is a measure of the sample error and is given by the formula cst\\ITI which is called the standard error or the standard error of the mean. Since the distribution of the means follows the pattern of a normal distribution, 95 percent of the sample means will lie within limits of two standard error on either side of the true or population means. Thus standard error of mean helps to judge whether the mean of a given sample is within the set confidence limit or not. The standard error indicates how reliable an estimate of the mean is likely to be. This is known as inferential statistics i.e. inferences are drawn about a population from study of just a sample from the same population. For example a researcher wants to forecast the results of an election on the basis of an opinion poll, or predict the effectiveness of a new drug for all patients after it has been tested on only a small sample. Now the problem in sampling is that it is unlikely that a sample will perfectly represent the population it is drawn from i.e. a statistic (such as the sample mean) will not exactly reflect its corresponding parameter (the population mean). For example is a sample of 100 people is drawn from a population with a mean height of 6 feet, it would not be expected that the mean height of the sample would exactly be 6 feet. This is known a sampling error- which is not an error, but just natural, expected random variation. So when we want to study a population, we draw a sample from the population under study. We calculate the mean of the sample. Now the next question arises that - How accurate is the mean of our sample? In order to answer these questions, we calculate the standard error of the mean and set up 'confidence limits' within which the mean (I), of the population is likely to lie. Example: Let's suppose, a random sample of 25 males, is drawn. Their mean temperature is 98.14 deg. F with a standard detion of 0.6. What can we say of the true mean of the population from which the sample is drawn. We use the standard en-or as the yard stick: S.E.27 = 0.6 TNIS = 0.12 We now set up confidence limits on the basis of the normal curve distribution. If the limits are set out at twice the standard error from the mean (95 percent confidence limits) the range of the population mean would be 98.14 (2 x 0.12) = 97.90 deg. to 98.38 deg.
Based on normal distribution
It depends on standard detion of mean
As the sample size increases, standard error will also increase
Used to estimate confidence limitmeasure