Question

A television network maintains that switching its highest rated situation comedy (sitcom) from Monday to Friday evening will have no effect on the show’s popularity, which is currently 88% of the viewing audience. The sponsor believes the change will damage the program’s rating. A trial Friday evening is agreed to and 90 homes in which someone is watching television are randomly surveyed. Of these viewers, 74 of them are watching the sitcom. At the 0.01 significance level, can we conclude that proportion of viewers is less than 88%?

1. What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

2. Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round the intermediate values and final answer to 2 decimal places.)

3. What is your decision regarding the null hypothesis?

Answer 1

Solution:

What is the decision rule? (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)

Answer: Reject H₀, if

Where:

is the left-tailed critical value at the 0.01 significance level.

Compute the value of the test statistic. (Negative amount should be indicated by a minus sign. Round the intermediate values and final answer to 2 decimal places.)

Answer: The value of the test statistic is:

Where:

  

What is your decision regarding the null hypothesis?

Answer: Since the test statistic does not fall in the rejection region, we, therefore, fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the proportion of viewers is less than 88%.