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 6 residents has a mean annual income of $41 ,000 and a standard deviation of $8400. In County B, a random sample of 8 residents has a mean annual income of $39,100 and a standard deviation of $5400. At a = 0.10. answer parts (a) through (e). Assume the population variances are not equal. If convenient, use technology to solve the problem. (b) Find the critical value(s) and identify the rejection region(s). Enter the critical value(s) below. E (Type an integer or decimal rounded to three decimal places as needed. Use a comma to separate answers as needed.) Select the correct rejection region(s) below. 0 A. t to O C. - to t':J (c) Find the standardized test statistic. t= E (Type an integer or decimal rounded to three decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. V the null hypothesis. (e) Interpret the decision in the context of the original claim. At the 10% signicance level, : enough evidence to support the personnel director's claim