Chapter 8, Problem 8.91LM

Independent random samples were selected from two normally distributed populations with means and respectively. The sample sizes, means, and variances are shown in the following table.

Sample 1	Sample 2
n1 = 12	n2 = 14
${\bar{x}}_1=17.8$	${\bar{x}}_2=15.3$
$s_1^2=74.2$	$s_2^2=60.5$

Test H₀: (μ₁ – μ₂) = 0 against H_a: (μ₁ – μ₂) > 0 by comparing α = .05 with the p-value of the test.

Form a 99% confidence interval for (μ₁ – μ₂).

How large must n₁and n₂ be if you wish to estimate (μ₁ – μ₂) 10 within 2 units with 99% confidence? Assume that n₁= n₂.