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 350 viewers. After viewing the shows, 250 indicated they would watch the new show and suggested it replace the crime investigation show.

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

Population proportion_________?

2. Develop a 99% confidence interval for the population proportion. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Confidence interval ______ and ________?

Answer 1

Here, 250 out of 350 indicated they would watch the new show and suggested it replace the crime investigation show.

a) We know that the population proportion can be estimated by the sample proportion.

Here, sample proportion , = 250 / 350

= 0.714

An estimated value of the population proportion is 0.714.

b) For a 99% confidence interval, the z-value is = 2.58

The confidence interval is = z * (1-)/n

= 0.714 (2.58 * 0.0241)

= 0.714 0.062

= ( 0.652 , 0.776 )

The confidence interval is (0.652 , 0.776).

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