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[All Steps] Ads. 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

Question: Ads. 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.

What are the hypotheses?
The station plans to conduct this test using a $10 \%$ level of significance, but the company wants the significance level lowered to $5 \%$. Why?
What is meant by the power of this test?
For which level of significance will the power of this test be higher? Why?
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.

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[All Steps] Ads. 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

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