Question: Attitudes toward school. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200 . The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. Their mean score is \(\bar{x}=132.2\)

1. Assuming that \(\sigma=30\) for the population of older students, carry out a test of
   \[\begin{aligned} & {{H}_{0}}:\mu =115 \\ & {{H}_{a}}:\mu >115 \\ \end{aligned}\]
   Report the \(P\) -value of your test, and state your conclusion clearly.
2. Your test in (a) required two important assumptions in addition to the assumption that the value of \(\sigma\) is known. What are they? Which of these assumptions is most important to the validity of your conclusion in (a)?

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