Question

0. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The SSHA scores for US college stu- dents are approximately normally distributed with a mean of 115 and standard deviation of 30. A researcher who suspects that students 30 years of age and older have better attitudes toward school gives the SSHA to 35 students who are at least 30 years of age. Their mean SSHA score is 124.8.

   (a) (13 pts) Using our 6-step process, test the hypothesis that the mean SSHA score for older students is greater than the national mean score.

   (b) (6 pts) Suppose that someone who ran a hypothesis test for part (a) made a Type II error. Explain what that error means in this context.

Answer 1

a. Here claim is that mean is greater than 115

So hypothesis is vs

As population standard deviation is known we will use z statistics

P value is

As P value is less than alpha=0.05, we reject the null hypothesis

Hence we have sufficient evidence to support the claim that mean is greater than 115.

b. Type II error is failing to reject the false null hypothesis

So in this context, mean is greater than 115, but we conclude that it is not greater than 115 and hence it is Type II error.