The Fox TV network is considering replacing one of its prime

The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show. Before a final decision is made, network executives commission a sample of 420 viewers. After viewing the comedy, 250 indicated they would watch the new show and suggested it replace the crime investigation show.

Develop a 99 percent confidence interval for the population proportion. (Round your answers to 3 decimal places.)

Solution

(a) Estimated population proportion= 250/420

=0.595

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(b) Given a=0.01, Z(0.005) = 2.58 (from standard normal table)

So a 99 percent confidence interval is

p+/- Z*sqrt(p*(1-p)/n)

--> 0.595 +/- 2.58*sqrt(0.595*(1-0.595)/420)

--> (0.533, 0.657)

Answer: The confidence interval is between 0.533 and 0.657 .