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 400 viewers. After viewing the comedy, 250 indicated they would watch the new show suggested it replace the crime investigation show.

For an 84.5% confidence interval, what is the upper confidence limit for the proportion who prefer the new show?
Express your sollutions as the decimal equivalent of a proportion rounded to four decimal places.

Answer 1

Solution :

Given that,

n = 400

x = 250

= x / n = 250 / 400 = 0.625

1 - = 1 - 0.625 = 0.375

At 84.5% confidence level the z is ,

= 1 - 84.5% = 1 - 0.845= 0.155

/ 2 = 0.155/ 2 = 0.0775

Z_/2 = Z_0.0775 = 1.422

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

= 1.422* (((0.625 * 0.375) / 400) = 0.0344

A 84.5 % confidence interval for population proportion p is ,

- E < P < + E

0.625 - 0.0344 < p < 0.625 + 0.0344

0.5906< p < 0.6594

The 84.5% confidence interval for the population proportion p is : ( 0.5906, 0.6594)