Chapter 5: Problem 6
Each of 51 golfers hit three golf balls of brand \(X\) and three golf balls of brand \(\mathrm{Y}\) in a random order. Let \(X_{i}\) and \(Y_{i}\) equal the averages of the distances traveled by the brand \(\mathrm{X}\) and brand \(\mathrm{Y}\) golf balls hit by the \(i\) th golfer, \(i=1,2, \ldots, 51\). Let \(W_{i}=X_{i}-Y_{i}, i=1,2, \ldots, 51 .\) To test \(H_{0}: \mu_{W}=0\) against \(H_{1}: \mu_{W}>0\), where \(\mu_{W}\) is the mean of the differences. If \(\bar{w}=2.07\) and \(s_{W}^{2}=84.63\), would \(H_{0}\) be accepted or rejected at an \(\alpha=0.05\) significance level? What is the \(p\) -value of this test?
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