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 490 viewers. After viewing the comedy, 420 indicated they would watch the new show and suggested it replace the crime investigation show.   

a. Estimate the value of the population proportion. (Round the final answer to 3 decimal places.)

Estimate of proportion           

b. Compute the standard error of the proportion. (Round the final answer to 3 decimal places.)

Standard error of the proportion             

c. Develop a 95% confidence interval for the population proportion. (Round the final answers to 3 decimal places.)

The confidence interval is between  and  .

d. Interpret your findings. (Round the final answers to the nearest whole number.)

We are reasonably sure the population proportion is between  and  %.

Answer 1

Solution :

Given that,

n = 490

x = 420

a) Point estimate = sample proportion = = x / n = 420 / 490 = 0.857

1 - = 1 - 0.857 = 0.143

b) =  [p( 1 - p ) / n] = [(0.857 * 0.143) / 490 ] = 0.016

c) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_{0.025 = 1.960}

Margin of error = E = Z _{/ 2} *

= 1.96 * 0.016

= 0.031

A 95% confidence interval for population proportion p is ,

± E  

= 0.857 ± 0.031

= ( 0.826, 0.888 )

The confidence interval is between 0.826 and 0.888 .

d) We are reasonably sure the population proportion is between 83% and 89%.