A personnel director in a particular state claims that the mean annual income is greater in one of the state's counties (county A) than it is in another county (county B). In County A, a random sample of 12 residents has a mean annual income of \( \$ 40,600 \) and a standard deviation of \( \$ 8100 \). In County B , a random sample of 10 residents has a mean annual income of \( \$ 38,000 \) and a standard deviation of \( \$ 5500 \). At \( \alpha=0.005 \), answer parts (a) through (e). Assume the population variances are not equal. If convenient, use technology to solve the problem. (a) Identify the claim and state \( \mathrm{H}_{0} \) and \( \mathrm{H}_{\mathrm{a}} \). Which is the correct claim below? A. "The mean annual income in county A is less than in county B." C. "The mean annual income in county A is greater than in county B." D. "The mean annual incomes in counties A and B are equal."
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