Question

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 1,187 responses, of which 616 indicate that they would like to see the new show in the lineup. A) Compute the value of the test statistic. B)Calculate the critical value at α = 0.10.

Answer 1

Let p denotes true proportion of customers who want to watch the new show.

To test against

Here

sample proportion

and sample size

The test statistic can be written as

which under H₀ follows a standard normal distribution.

We reject H₀ at 10% level of significance if

Now,

The value of the test statistic =

and critical value =

Since , so we reject H₀ at 10% level of significance and we can conclude that majority of the customers want to watch the new show.