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 450 viewers. After viewing the shows, 200 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.)

2. Develop a 98% confidence interval for the population proportion. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Answer 1

Solution :

Given that,

n = 450

x = 200

a)

Point estimate = sample proportion = = x / n = 0.444

1 - = 0.556

b)

At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= 2.326 * (((0.444 * 0.556) / 450)

= 0.054

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.444 - 0.054 < p < 0.444 + 0.054

0.390 < p < 0.498

The 98% confidence interval for the population proportion p is : (0.390 , 0.498)