Question

A major exam company retains the ACT scores for all test takers for the last year. The mean composite ACT score for last year was 21.0 with a standard deviation of 5.4.

a. If were to create a sampling distribution from this data with samples of 30 exams from the data, what would the shape, mean, and standard deviation of distribution be? Why?

b. Would the shape, mean, or standard deviation of the sampling distribution vary if our sample size increased to 100 exams? If so, which ones would vary and why?

Answer 1

Answer: (a) 0.9858 (b) 0.54

Explanation:

μ = 21.0, σ = 5.4

a) The shape of the sampling distribution would be approximately normal, the mean of the smaple would be 21.0 and standard deviation of the sample would be 0.9859.

S.D = \frac{\sigma }{\sqrt{n}}

S.D = \frac{5.4 }{\sqrt{30}}

S.D = 0.9859

b) The shape of the sampling distribution would be approximately normal, the mean of the smaple would be 21.0 and standard deviation of the sample would be 0.54.

S.D = \frac{\sigma }{\sqrt{n}}

S.D = \frac{5.4 }{\sqrt{100}}

S.D = 0.54

The sample standard deviation would vary becuase as the sample size increases the sample S.D decreases.