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 300 viewers. After viewing the shows, 150 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 answers to 3 decimal places.)

b. Develop a 95% confidence interval for the population proportion. (Use z Distribution Table.) (Round Z-score to 2 decimal places and final answers to 3 decimal places.)

Answer 1

Solution :

Given that,

a.

Point estimate = sample proportion = = x / n = 150 / 300 = 0.500

1 - = 1 - 0.500 = 0.5

Z_/2 = 1.96

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.96 * (((0.500 * 0.5) / 300)

Margin of error = E = 0.057

b.

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.500 - 0.057 < p < 0.500 + 0.057

0.443 < p < 0.557

The 95% confidence interval for the population proportion p is : 0.443 , 0.557