The Fox TV network is considering replacing one of its prime-time crime investig

Question

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 390 viewers. After viewing the comedy, 230 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.)

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 390 viewers. After viewing the comedy, 230 indicated they would watch the new show and suggested it replace the crime investigation show.

Explanation / Answer

(a)Estimated population proportion =230/390 =0.590

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(b) Given a=1-0.99=0.01, Z(0.005) =2.58 (from standard normal table)

So the lower bound is

p -Z*sqrt(p*(1-p)/n) =0.5897436-2.58*sqrt(0.5897436*(1-0.5897436)/390) =0.525

So the upper bound is

p +Z*sqrt(p*(1-p)/n) =0.5897436+2.58*sqrt(0.5897436*(1-0.5897436)/390)=0.654

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