The mayor of a particular city recently claimed in a press conference that he ha

Question

The mayor of a particular city recently claimed in a press conference that he had done a tremendous job of boosting the city's economy with his policies. As evidence, he claimed that the average income for an adult city resident was $62000, which was far more than the rest of the region. An editor at the newspaper believes that the mayor's claim is too high and that the average income for city residents is actually lower. To test this, a random sample of 65 adult city residents was selected. The sample average income was $54590 and the sample standard deviation was $18632. Can the newspaper editor dispute the mayor's claim? Use a 1% significance level to test. What are the correct hypotheses?

Explanation / Answer

here n = 65>30 therefore the z stat normal hypothesis test will be done

the null hypothesis = Ho= u = 62000

the alternate hypothesis = Ha = u <62000

alpha = 0.01

the critical region = z<-2.33

the z stat = (54590 - 62000) / 18632 = -0.40

hence as z stat = -0.40> -2.33

therefore we will not reject the null hypothesis

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