The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitudes toward school. Scores range from 0 to 200. The mean score for college students is about 115.8, and the standard deviation is about 32.9. A teacher suspects that the mean μ for older students is higher than 115.8. She gives the SSHA to an SRS of 25 students who are at least 30 years old. Suppose we know that scores in the population of older students are Normally distributed with standard deviation σ = 32.9.

Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students' study habits and attitudes toward school. Scores range from 0 to 200. The mean score for college students is about 115.8, and the standard deviation is about 32.9. A teacher suspects that the mean μ for older students is higher than 115.8. She gives the SSHA to an SRS of 25 students who are at least 30 years old. Suppose we know that scores in the population of older students are Normally distributed with standard deviation σ = 32.9.

We seek evidence against the claim that μ = 115.8. What is the sampling distribution of the mean score of a sample of 25 students if the claim is true?

The distribution is

a) Binomial

b) Normal

with mean =

and standard deviation (±0.0001) =

Answer 1

The sampling distribution of the mean score of a sample of 25 students follows a normal distribution if the claim that μ = 115.8 is true.

Mean of the sampling distribution (μ): The mean score for college students is about 115.8, so the mean of the sampling distribution would also be 115.8.

Standard deviation of the sampling distribution (σ): The standard deviation of the population of older students is σ = 32.9. When sampling, the standard deviation of the sampling distribution is given by σ / sqrt(n), where n is the sample size. In this case, the sample size is 25, so the standard deviation of the sampling distribution is 32.9 / sqrt(25) = 6.58 (approximately).