A personnel director from Pennsylvania claims that the mean household income is greater in Allegheny County than it is in Erie County. In Allegheny County, a sample of 19 residents has a mean household income of $49,700 and a standard deviation of $8800. In Erie County, a sample of 15 residents has a mean household income of $42,000 and a standard deviation of $5100. At α = 0.05, can you support the personnel director’s claim? Assume the population variances are not equal.
(a) Identify the claim and state H0 and Ha,
(b) Find the critical value(s) and identify the rejection region(s),
(c) Find the standardized test statistic t,
(d) Decide whether to reject or fail to reject the null hypothesis,
(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed. If convenient, use technology.
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