After a college football team once again lost a game to their archrival,the alumni association conducted a survey to see if alumni were in favor of firing the coach.A simple random sample of 100 alumni from the population of all living alumni was taken.Sixty-four of the alumni in the sample were in favor of firing the coach.Let p represent the proportion of all living alumni who favored firing the coach.Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach.To do this they test the hypotheses H₀: p = 0.50 versus H_a: p 0.50.The alumni association wished to conduct the test at a 5% significance level.What would their decision be? Based on that decision,what type of mistake could they have made? A)Do not reject H₀;Type I error B)Do not reject H₀;Type II error C)Reject H₀;Type I error D)Reject H₀;Type II error

Question

After a college football team once again lost a game to their archrival,the alumni association conducted a survey to see if alumni were in favor of firing the coach.A simple random sample of 100 alumni from the population of all living alumni was taken.Sixty-four of the alumni in the sample were in favor of firing the coach.Let p represent the proportion of all living alumni who favored firing the coach.Suppose the alumni association wished to see if the majority of alumni are in favor of firing the coach.To do this they test the hypotheses H₀: p = 0.50 versus H_a: p > 0.50.The alumni association wished to conduct the test at a 5% significance level.What would their decision be? Based on that decision,what type of mistake could they have made? A)Do not reject H₀;Type I error B)Do not reject H₀;Type II error C)Reject H₀;Type I error D)Reject H₀;Type II error

Quizplus · Accepted Answer

Since 64% of the sample favors firing the coach, which is greater than the 50% threshold, the decision would be to reject the null hypothesis that p = 0.50 in favor of the alternative hypothesis that p > 0.50. By rejecting the null hypothesis, the type of mistake that could be made is a Type I error, which occurs when the null hypothesis is true but is incorrectly rejected.

After a College Football Team Once Again Lost a Game