You have a population that has a mean of 100 and a standard deviation of 15. You randomly draw 100 people out of this population and record the mean score. You repeat the process a large number of times recording the mean score for each sample you draw. What will be the standard deviation of this set of many means that you have drawn?
The standard deviation of the set of many means that you have drawn is known as the standard error of the mean (SEM). It can be calculated using the formula:
SEM = standard deviation / square root of sample size
In this case, the population has a standard deviation of 15. Since you are randomly drawing 100 people out of this population for each sample, the sample size is 100. Therefore, we can calculate the SEM as follows:
SEM = 15 / √100 = 15 / 10 = 1.5
So, the standard deviation of the set of many means that you have drawn will be 1.5.