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A magazine claims that its readers have an average annual income of $43,725 with a standard...

A magazine claims that its readers have an average annual income of $43,725 with a standard deviation of $3,456. You randomly sample on 27 of the magazine’s readers and an average income of $38,251. Determine if the income of the readers is significantly less than the income claimed by the company using  = 0.01 and the prob-value approach.

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(1)Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: μ-43725 Ha: < 43725 This corresponds to a left-tailed test, for which a z-test for one mean, with known population standard deviation will be used. (2) Rejection Region Based on the information provided, the significance level is a 0.01, and the critical value for a left- tailed test is ze2.33. The rejection region for this left-tailed test is R-z: z<-2.33 (3)_Test Statistics The z-statistic is computed as follows: X o 38251 -43725 3456/27 (4) Decision about the null hypothesis Since it is observed that z8.232.33, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p 0, and since p-00.01, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean is less than 43725, at the 0.01 significance level.

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