A real estate agent claims that there is no difference between the mean household incomes of two neighborhoods. The mean income of 12 randomly selected households from the first neighborhood is $32,750 with a standard deviation of $1900. In the second neighborhood, 10 randomly selected households have a mean income of $31,200 with a standard deviation of $1825. At α = 0.01, can you reject the real estate agent’s claim? Assume the population variances are 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.