The following output (from \(\mathrm{R}\) ) presents the results of a hypothesis test for the difference \(\mu_{X}-\mu_{Y}\) between two population means:

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. Use the value of \(t\) and the mean of the differences in the output to compute the standard deviation \(s_{D}\) of the differences.

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Paired t-test data: x and y t = 1.9577, df = 11, p-value = 0.038058 alternative hypothesis: true difference in means is greater than 0 95 percent confidence interval: 2.77938 Inf sample estimates: mean of the differences 33.632