Math  /  Data & Statistics

QuestionA personnel director in a particular state claims that the meanannual 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 18 residents has a mear annual income of $40,800\$ 40,800 and a standard deviation of $8800\$ 8800. In County B, a random sample of 8 residents has a mean annual income of $37,600\$ 37,600 and a standard deviation of $5800\$ 5800. At α=0.10\alpha=0.10, answer parts (a) through (e). Assum the population variances are not equal. If convenient, use technology to solve the problem.
The alternative hypothesis, Ha\mathrm{H}_{\mathrm{a}} (b) Find the critical value(s) and identify the rejection region(s).
Enter the critical value(s) below. 1.415 (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. A. t<t0,t>t0t<-t_{0}, t>t_{0} B. t>t0t>t_{0} C. t<t0t<-t_{0} D. t0<t<t0-t_{0}<t<t_{0}

Studdy Solution
Identify the rejection region(s) based on the critical value.
Since this is a one-tailed test with the alternative hypothesis μ1>μ2\mu_1 > \mu_2, the rejection region is for t>t0t > t_0.
Correct rejection region: B. t>t0t > t_0
The critical value is 1.4151.415, and the rejection region is t>1.415t > 1.415.

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