Critical value approach (predetermined value of the significance level alpha) Th

Question

Critical value approach (predetermined value of the significance level alpha) The mayor of a large city claims that the average net worth of families living in this city is at least $300,000. A random sample of 36 families selected from this city produced a mean net worth of $282,000. Assume that the net worths of all families in this city have a normal distribution with the population standard deviation of $70,000. Using a 2.5% significance level, can you conclude that the mayor s claim is false?

Explanation / Answer

To test mayor' sclaim, perform 1-sample Z test. (Population standard deviation is known)

Z=(Xbar-mu)/(sigma/sqrt N), where, Xbar is sample mean, mu is population mean, sigma is population standard deviation and N is sample size.

=(282000-30000)/(70000/sqrt 36)

=-1.54

The p value is 0.06178. The p value is not less than alpha=0.025. Therefore, fail to reject null hypothesis. There is not sufficient sample evidence to support mayor's claim.

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