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 500 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 the z-values to 2 decimal places. Round your answer to 3 decimal places.)

B) Develop a 90% confidence interval for the population proportion. (Use z Distribution Table.) (Round the z-values to 2 decimal places. Round your answers to 3 decimal places.)

Answer 1

Solution:

Given:

n = 500

x = Number of viewers  indicated they would watch the new show and suggested it replace the crime investigation show

x = 250

Part A) Estimate the value of the population proportion.

Part B) Develop a 90% confidence interval for the population proportion.

Formula:

where

Z_c is z critical value for c = 90% confidence level.

Find Area = ( 1 + c ) / 2 = ( 1 + 0.90) / 2 = 1.90 / 2 = 0.9500

Look in z table for Area = 0.9500 or its closest area and find corresponding z value.

Area 0.9500 is in between 0.9495 and 0.9505 and both the area are at same distance from 0.9500

Thus we look for both area and find both z values

Thus Area 0.9495 corresponds to 1.64 and 0.9505 corresponds to 1.65

Thus average of both z values is : ( 1.64+1.65) / 2 = 1.645

Thus Z_c = 1.645

Thus

Thus

Thus a 90% confidence interval for the population proportion is