## Elementary Statistics (12th Edition)

$H_{0}:p=75$%=0.75. $H_{a}:p>0.75.$ $\hat{p}$ is the number of objects with a specified value divided by the sample size. Hence $\hat{p}=0.77.$ The test statistic is:$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.77-0.75}{\sqrt{0.75(1-0.75)/25000}}=7.3.$ The P is the probability of the z-score being more than 7.3 which is 1 minus the probability of the z-score being less than 7.3, hence:P=1-0.9999=0.0001. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P=0.0001 is less than $\alpha=0.01$, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that more than 75% of the TVs used were tuned to the Super Bowl.