Question

consider a sample of 49 football games, where 27 of them were won by the home team. use a 0.01 significance level to test the claim that the probability that the home team wins is greater than 0.5.

identify the test statistic for this hypothesis test.
the test statistic for this hypothesis test is 0.71
(round to two decimal places as needed.)

identify the p - value for this hypothesis test.
the p - value for this hypothesis test is 0.239
(round to three decimal places as needed.)

identify the conclusion for this hypothesis test.

Explanation:

Step1: Determine the decision rule

In hypothesis testing, if the P - value > significance level ($\alpha$), we fail to reject the null hypothesis ($H_0$). Here, $\alpha = 0.01$ and the P - value is $0.239$.

Step2: Make a conclusion

Since $0.239>0.01$ (P - value > $\alpha$), we fail to reject $H_0$. When we fail to reject $H_0$, it means there is not sufficient evidence to support the alternative hypothesis. The alternative hypothesis in a test for $p > 0.5$ (the claim that the probability that the home team wins is greater than $0.5$) is $H_1:p > 0.5$.

Answer:

B. Fail to reject \(H_0\). There is not sufficient evidence to support the claim that the probability of the home team winning is greater than one - half.