The Fox TV network is considering replacing one of its prime

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, 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 answer to 3 decimal places.)

B. Develop a 95% confidence interval for the population proportion. (Use z Distribution Table.) (Round your answers to 3 decimal places.)

Solution

Answer to the question)
given:

Total n = 450

People who would watch the new show x = 150

.

Thus sample proportion p^ = x/n

p^ = 150/450 = 0.3333

.

SE = sqrt(p^*(1-p^)/n)

SE = sqrt(0.3333 *0.6667 /450)

SE = 0.0222

.

Formula of confidence interval is:

p^ - z* SE , p^ + z* SE

.

We need to find 95% confidence interval , for it the Z critical value is 1.96

.

Thus on plugging all the values we get:

0.3333 -1.96 *0.0222 , 0.3333 + 1.96*0.0222

0.289788 , 0.376812