A personnel director from Hawaii claims that the mean household income is the same in Kauai County and Maui County. In Kauai County, a sample of 18 residents has a mean household income of $56,900 and a standard deviation of $12,100. In Maui County, a sample of 20 residents has a mean household income of $57,800 and a standard deviation of $8000. At α = 0.10, can you reject the personnel director’s claim? Assume the population variances are not equal.

(a) Identify the claim and state H₀ and H_a,

(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.