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.What is the P-value for this hypothesis test? A)Below 0.001 B)0.0026 C)0.0682 D)0.14

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.What is the P-value for this hypothesis test? A)Below 0.001 B)0.0026 C)0.0682 D)0.14

Quizplus · Accepted Answer

The P-value is calculated using the standard normal distribution. With 64 out of 100 alumni in favor, the sample proportion is 0.64. The standard error is calculated as sqrt(0.5*0.5/100) = 0.05. The z-score is (0.64-0.5)/0.05 = 2.8. The P-value for a z-score of 2.8 is approximately 0.0026.

After a College Football Team Once Again Lost a Game