Chapter 8.2, Problem 8.3LM

In order to compare the means of two populations, independent random samples of 400 observations are selected from each population, with the following results:

Sample 1	Samlpe 2
${\bar{x}}_1$ = 5,275	${\bar{x}}_2$ = 5,240
s1 = 150	s2 = 200

1. a. Use a 95% confidence interval to estimate the difference between the population means (μ₁ – μ₂). Interpret the confidence interval.
2. b. Test the null hypothesis H₀ : (μ₁ – μ₂) = 0 versus the alternative hypothesis H₀ : (μ₁ – μ₂) ≠ 0. Give the significance level of the test and interpret the result.
3. c. Suppose the test in part b was conducted with the alternative hypothesis H₀ : (μ₁ – μ₂) > 0. How would your answer to part b change?
4. d. Test the null hypothesis H₀ : (μ₁ – μ₂) = 25 versus H₀ : (μ₁ – μ₂) ≠ 25. Give the significance level and interpret the result. Compare your answer with the test conducted in part b.
5. e. What assumptions are necessary to ensure the validity of the inferential procedures applied in parts a-d?