Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a Normal distribution with mean 115 and standard deviation σ = 25. You suspect that incoming freshmen have a mean μ, which is different from 115, because they are often excited and anxious about entering college. To test your suspicion, you test the following hypotheses:

H₀: μ = 115, H_a: μ ≠ 115

You give the SSHA to 25 students who are incoming freshmen and find their mean score is 116.2. The P-value of your test is:

0.1151.

0.2302.

0.4052.

0.8104.

Answer 1

The provided sample mean is 116.2 and the known population standard deviation is 25, and the sample size is n = 25.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ=115

Ha: μ≠​115

This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.

(2) Test Statistics

The z-statistic is computed as follows:

Using the P-value approach: The p-value is p = 0.8104