Statistics 8

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To solve use a confidence level of proportion.
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 380
viewers. After viewing the comedy, 225 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.)

Solution: sample size(n) = 380

Pop. Proportion = 225/380 = 0.592

(b) Develop a 90 percent confidence interval for the population proportion.
(Round your answers to 3 decimal places.)

Solution: Let X = the number of people want a new show. X is binomial. X ~ B(380, 225/380)

To calculate the confidence interval, you must find p', q', and EBP.

n = 380

x = the number of successes = 225

p’ = 225/380 = 0.592

q'=1−p'=1−0.592 = 0.408

Since Confidence level(CL)=0.90, then α =1−CL=1−0.90= 0.1

α /2 = 0.1/2 = 0.05

z.05=1.64 using a calculator, computer, or standard normal table.

Remember that the area to the right = 0.05 and therefore, area to the left is 1 – 0.05 = 0.95

The z-score that corresponds to 0.95 is 1.65.

The error bound for a proportion is EBP = z α /2 * sqrt [( p’ * q’)/n]

= 1.65 * sqrt [(0.592*0.408)/380]

= 1.65 * 0.0252

= 0.04159 = 0.042

P’ – EBP = 0.592 - 0.042 = 0.550

P’ + EBP = 0.592 + 0.042 = 0.634