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

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.

(a)

Estimate the value of the population proportion. (Round your answer to 3 decimal places.)

  Estimated population proportion =250/420 =0.595

(b)

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

Confidence Interval Estimate for the Proportion

Data

Sample Size

420

Number of Successes

250

Confidence Level

99%

Intermediate Calculations

Sample Proportion

0.595

Z Value

2.576

Standard Error of the Proportion = sqrt(0.595*(1-0.595)/420))=

0.0240

Interval Half Width=2.576*0.024 =

0.0618

Confidence Interval

Interval Lower Limit=p-width=

0.5332

Interval Upper Limit=p+width=

0.6568

  The confidence interval is between 0.533 and 0.657