Question

A company is willing to renew its advertising contract with a local radio station only if

the station can prove that more than 16% 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 347 people. The survey shows that 90 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)

Answer 1

To find the value of p, we need to calculate the sample proportion and compare it to the critical value.

Step-by-step explanation:

In this question, we are testing the proportion of residents in a city who have heard the ad and recognize the company's product. The null hypothesis (H0) states that the proportion is 16%, while the alternative hypothesis (H1) states that the proportion is greater than 16%. We are given that the survey of 347 people shows that 90 people have heard the ad and recognize the company's product. To find the value of p, we need to calculate the sample proportion and compare it to the critical value.

First, we calculate the sample proportion: p = 90/347 ≈ 0.2595. Now, we need to compare this to the critical value. The critical value for a 5% significance level is Z0.05 = 1.645. Since the sample proportion (0.2595) is greater than p (0.16), we reject the null hypothesis and conclude that there is sufficient evidence to renew the advertising contract.