## Related questions with answers

A company is willing to renew its advertising contract with a local radio station only if the station can prove that more than 20% 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 400 people. a) What are the hypotheses? b) The station plan s to conduct this test using a 10% level of significance, but the company wants the significance level lowered to 5%. Why? c) What is meant by the power of this test? d) For which level of significance will the power of this test be higher? Why? e) They finally agree to use

$\alpha = 0.05$

, but the company proposes that the station call 600 people instead of the 400 initially proposed. Will that make the risk of Type II error higher or lower? Explain.

Solution

Verified(a) Given claim: proportion is more than 20%

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

$H_0:p=20\%=0.20$

$H_a:p>0.20$

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