consider a sample of 51 football games, where 31 of them were one by the home team. Use a 0.01 significant level to test the claim that the probability that the home team wins is greater than one-half. B. \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array} \] c. \[ \begin{array}{l} H_{0}: p>0.5 \\ H_{1}: p=0.5 \end{array} \] D. \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p<0.5 \end{array} \] Identify the test statistic for this hypothesis test. The test stafistic for this hypothesis test is $\mathbf{1 . 5 4}$. (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The P-value for this hypothesis test is 0.062 . (Round to three decimal places as needed.) Identify the conclusion for this hypothesis test. A. Fal to reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half. B. Fall to reject $\mathrm{H}_{0}$. There is sufficient evidence to support the claim that the probability of the home team winning is greater than one half. c. Reject $\mathrm{H}_{0}$. There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half. D. Reject $\mathrm{H}_{0}$. There is sufficient evidence fo support the claim that the probability of the home team winning is greater than one-half.
Solution
Step 1 ：The null hypothesis is usually a statement of no effect or no difference. In this case, it would be that the probability of the home team winning is equal to one-half. The alternative hypothesis is what we are testing against the null hypothesis. In this case, it would be that the probability of the home team winning is greater than one-half. So, the correct null and alternative hypotheses for this problem are: \[H_{0}: p=0.5\] and \[H_{1}: p>0.5\].
Step 2 ：The test statistic for this hypothesis test is \(1.54\).
Step 3 ：The P-value for this hypothesis test is \(0.062\).
Step 4 ：Since the P-value is greater than the significance level of \(0.01\), we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one-half.
Step 5 ：Final Answer: \[\boxed{H_{0}: p=0.5, H_{1}: p>0.5}\]
