Question

A personnel director in a particular state claims that the mean annual income is the same in one of the​ state's counties​ (County A) as it is in another county​ (County B). In County​ A, a random sample of 15 residents has a mean annual income of $ 40 comma 800 and a standard deviation of $ 8800. In County​ B, a random sample of 9 residents has a mean annual income of $ 38 comma 100 and a standard deviation of $ 5500. At alphaequals0.01​, answer parts​ (a) through​ (e). Assume the population variances are not equal. Assume the samples are random and​ independent, and the populations are normally distributed. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). ​(c) Find the standardized test statistic. ​(d) Decide whether to reject or fail to reject the null hypothesis. ​(e) Interpret the decision in the context of the original claim.

Answer 1

Conclusion : There is not sufficient evidence to warrant the rejection of the claim that the mean annual income is the same in one of the​ state's counties​ (County A) as it is in another county​ (County B).