Question: The director of admissions at the University of Maryland, University College is concerned about the high cost of textbooks for the students each semester.  A sample of 20 students enrolled in the university indicates that X (bar) = $315.4 and s = $43.20.

1. We need to test:
   \[\begin{aligned} & {{H}_{0}}:\mu \le 300 \\ & {{H}_{A}}:\mu >300 \\ \end{aligned}\]
   at the 0.10 significance level. We use a right-tailed t-test. The t-statistics is computed as
   \[t=\frac{\bar{X}-\mu }{s/\sqrt{n}}=\frac{315.4-300}{43.20/\sqrt{20}}=1.5942\]
   The critical right-tailed t-value, for \(\alpha =0.10\) and 19 degrees of freedom is equal to
   \[{{t}_{c}}=1.3277\]
   Since \(t>{{t}_{c}}\), we reject the null hypothesis, which means that we have enough evidence to claim that the population mean is above $300.
2. What is your answer in (a) if s = $75 and the 0.05 level of significance is used?
3. What is your answer in (a) if X (bar) = $305 and s = 43.20?
4. Based on the information in part (a), what decision should the director make about the books used for the courses if the goal is to keep the cost below $300?

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