Question

After the football team once again lost a game to the college's arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. A random sample of 100 alumni from the population of all living alumni was taken. 64 of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach.

a) Give a 95% confidence interval for p.

b) Suppose you wished to test if the majority of alumni are in favor of firing the coach.

i) State the null and alternative hypotheses
ii) Calculate the test statistic.
iii) Find the p-value. Do the sample data give good evidence that the majority of alumni are in favor of firing the coach? Explain your reasoning.

Answer 1