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 comedy, 200 indicated they would watch the new show and suggested it replace the crime investigation show.

b. Develop a 98% 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 that,

Point estimate = sample proportion = = x / n = 200 / 450 = 0.444

Z_/2 = 2.33

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

= 2.33 * (((0.444 * 0.556) / 450)

= 0.055

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.444 - 0.055 < p < 0.444 + 0.055

0.389 < p < 0.499

(0.389 , 0.499)