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In: Statistics and Probability

1. Economists often track employment trends by measuring the proportion of people who are “underemployed,” meaning...

1. Economists often track employment trends by measuring the proportion of people who are “underemployed,” meaning they are either unemployed or would like to work full time but are only working part-time. In the summer of 2019, 18.5% of Americans were “underemployed.” The mayor of Detroit wants to show the voters that the situation is not as bad in his city as it is in the rest of the country. His staff takes a simple random sample of 400 Detroit residents and finds that 60 of them are underemployed.  

(a) Does the data give convincing evidence that the proportion of underemployed in Detroit is lower than elsewhere in the country? Perform the appropriate statistical test.

(b) The mayor’s political rival claims that the same poll actually fails to provide sufficient evidence that the underemployment rate in Detroit is any different from the rest of the country. Explain how it is possible for him to come to this conclusion.

(c) Suppose the true underemployment rate in Detroit is actually only 14%. If the mayor were to perform the exact same test again, what is the probability that the mayor’s test results in a Type II Error at the 5% level?

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orchestra answered 1 year ago
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