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?
Standard error of the mean is the standard deviation of the sampling distribution of the means.
Take the standard deviation (15) and divide by the square root of the sample size (100) for your answer.
1.5
To find the standard deviation of the set of sample means, we can use the concept of the standard error of the mean (SEM). The SEM represents the average amount by which the sample means deviate from the population mean.
The formula to calculate the SEM is given by: SEM = standard deviation / sqrt(sample size)
In this case, the standard deviation of the population is 15 and the sample size is 100. Plugging in the values to the formula, we get:
SEM = 15 / sqrt(100) = 15 / 10 = 1.5
Therefore, the standard deviation of the set of means for the samples of size 100 drawn from this population will be 1.5.