The scores of high school seniors on the ACT college entranc

The scores of high school seniors on the ACT college entrance examination in a recent year had mean = 22.3 and standard deviation = 5.2. The distribution of scores is only roughly Normal. Now consider an SRS of 16 students who took the test. What are the mean and standard deviation of the sample mean score of these 16 students? Fill in the blanks (give exact answers): 1) The mean is: _______ . (Give your answer to 2 decimal places) 2) The standard deviation is: _______ . (Give your answer to 1 decimal places)

Solution

According to the central limit theorem, it has the same mean:

Mean = 22.3 [ANSWER]

However, the standard deviation will be divided by sqrt(n),

Sx = s / sqrt(n) = 5.2/sqrt(16) = 1.3 [ANSWER]