Question

Ads: A company is willing to renew it advertising contact with a local radio station only if the station can prove that more than 20% of the residents of the city heard the ad and not recognize the company’s product. The radio station conducts a random phone survey of 400 people.

A) What are the hypotheses

B) The station plans to conduct this test using a 10% level of significance, but the company wants the significance level lowered to 5%?

C) What is meant by the power of the test?

D) For which level of significance will the power of the test be higher? Why?

E) They finally agree to use a = 0.05, but the company proposes that the station call 600 people instead of the 400 initially proposed. With that make the risk of Type II error higher or lower? Explain

Answer 1

A) Say p0 is the proportion of residents of the city who have heard the ad but not recognized the company's product

Null Hypothesis: p0 <= 0.2

Alternate Hypothesis: p0 > 0.2

B) The significance level of the test is that the probability of committing a type 1 error, that is, incorrectly rejecting a true null hypothesis. Company wants to decrease the probability of committing this error from 10% to 5%

C) Power of the test is the probability of not committing a type 2 error, that is, not rejecting a false null hypothesis.

D) The power of the test will be higher in-case of the higher significance level, that is when the significance level, alpha was 0.10 because the region of acceptance gets lower in the case of alpha = 0.1 leading to less probability of a type 2 error.

E) Increasing the sample size leads to increase in power because a larger sample size narrows the distribution of the test statistic.