The following output (from \(\mathrm{R}\) ) presents the results of a hypothesis test for the difference between two 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 \(1 \%\) level? How can you tell?

d. If a \(98 \%\) confidence interval were computed for \(\mu_{X}-\mu_{Y}\), would it contain zero? How can you tell?

e. Use the output to compute the \(P\)-value using a \(z\) test. Are the results similar?

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Welch Modified Two-Sample t-Test data: x and y t = 2.4883, df = 90.746, p-value = 0.01466 alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: 0.6605194 5.8896264 sample estimates: mean of x mean of y 23.31843 20.04336