The following output (from \(\mathrm{R}\) ) presents the results of a hypothesis test for a population mean \(\mu\).

a. Is this a one-tailed or a two-tailed test?

b. What is the null hypothesis?

c. Can \(H_{0}\) be rejected at the \(5 \%\) level? How can you tell?

d. The sample standard deviation is \(s=1.29\). Use the value of \(s\) along with the output to compute the \(P\)-value for testing \(H_{0}: \mu \leq 87.5\) versus \(H_{1}: \mu>87.5\).

e. Someone suggests using a \(z\) test for these data, even though the population standard deviation is unknown. Explain why this is not a good idea.

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One Sample t-test data: X t = 0.51988, df = 4, p-value 0.3153 alternative hypothesis: true mean is greater than 90 95 percent confidence interval: 89.06979 Inf sample estimates: mean of x 90.3 =