Final answer:
The correct alternative hypothesis for testing if more than 71% of Kentucky alum believe the 2015 Wildcats are the greatest team of the 21st century is 'p > 0.71'. The null hypothesis is rejected if the p-value is less than the 0.10 significance level.option D is correct answer.
Step-by-step explanation:
The question pertains to hypothesis testing in statistics, specifically testing the proportion of Kentucky alum who believe the 2015 Wildcats are the greatest team of the 21st century. The alternative hypothesis for testing if more than 71% of the alums believe this should reflect the idea that the true proportion is greater than the specified value of 0.71. Hence, the correct alternative hypothesis is 'p > 0.71'.
To conduct the hypothesis test at the 0.10 level, we will assume that the null hypothesis is 'p ≤ 0.71' (the proportion is 71% or lower). The alternative hypothesis, as stated, is 'p > 0.71' (choice D), which means we are looking for evidence that the proportion is actually higher than 71%. If the test statistic calculated from the sample data falls into the critical region, we would then reject the null hypothesis in favor of the alternative.
The criterion for rejection of the null hypothesis in this case is a p-value less than the significance level of 0.10. If the calculated p-value is indeed lower, it implies that the sample evidence is strong enough to assert that a larger proportion of Kentucky alum believe in the 2015 Wildcats' supremacy compared to what was hypothesized under the null.