Question

A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 26% of the residents of the city have heard the ad and recognize the company's product. The radio station conducts a random phone survey of 500 people. The survey shows that 91 people have heard the ad and recognize the company's product. For this test, the radio station uses a 5% significance level and will reject the null hypothesis (will renew the contract) for any sample proportion that is greater than p. What is the value of p in the test (assume Z0.05 1.645)? Note: 1- Round any intermediate numbers to 4 decimal places. 2- Round your final answer to 3 decimal places. Enter your final answer with 3 decimal places. 3-Your final answer (proportion) should not be stated a percentage.

Answer 1

Solution :

x = 91

n = 500

$\hat p$ = x / n = 91 / 500 = 0.182