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. Compute the \(P\)-value using a \(z\) test. Are the results similar?

e. The sample standard deviation is \(s=21.2\). Use the value of \(s\) along with the output to compute the \(P\)-value for testing \(H_{0}: \mu=0\) versus \(H_{1}: \mu eq 0\).

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One-sample t-Test data: X t = 1.7303, df = 159, p-value 0.08552 alternative hypothesis: true mean is not equal to 1 95 percent confidence interval: 0.5898922 7.2101078 sample estimates: mean of x 3.9 =