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The Employment and Training Administration reported the U.S. mean unemployment insurance benefit of 238perweek(TheWorldAlmanac,2003).AresearcherinthestateofVirginiaanticipatedthatsampledatawouldshowevidencethatthemeanweeklyunemploymentinsurancebenefitinVirginiawasbelowthenationallevel.238 per week (The World Almanac, 2003). A researcher in the state of Virginia anticipated that sample data would show evidence that the mean weekly unemployment insurance benefit in Virginia was below the national level.

a.DevelopappropriatehypothesessuchthatrejectionofH0willsupporttheresearcherscontention.a. Develop appropriate hypotheses such that rejection of H0 will support the researcher’s contention.


$b. For a sample of 100 individuals, the sample mean weekly unemployment insurance benefit was 231 dollar with a sample standard deviation of 80 dollar. What is the$p$-value?$
$c. At$\alpha= .05$, what is your conclusion?$
$ d. Repeat the preceding hypothesis test using the critical value approach

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Given:

  • x\overline{x} = Sample mean = 231
  • ss = Sample standard deviation = 80
  • nn = Sample size = 100
  • α\alpha = Significance level = 0.05

In this exercise, we determine the conclusion of a hypothesis test about a population mean when the population standard deviation σ\sigma is unknown.

How do you execute a hypothesis test?

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