A demographics researcher claims that the mean household income in a recent year is greater in Cuyahoga County, Ohio, than it is in Wayne County, Michigan. In Cuyahoga County, a sample of 19 residents has a mean household income of $45,600 and a standard deviation of $2800. In Wayne County, a sample of 15 residents has a mean household income of $41,500 and a standard deviation of $1310. At α = 0.05, can you support the demographics researcher’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, and 

(e) Interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.