A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather watch. The network will keep its current lineup of shows unless the majority of the customers want to watch the new show. The network receives 827 responses, of which 428 indicate that they would like to see the new show in the lineup.

a. Set up the hypotheses to test if the television network should give its newest television shows a spot during prime viewing time at night.

b. Compute the value of the test statistic.

c. Define the rejection region(s) at α = 0.01.

d. What should the television network do?