Chapter 8.3, Problem 8.26LM

A paired difference experiment produced the following results

n_d = 38 ${\bar{x}}_1=92$ ${\bar{x}}_2=95.5$ $\bar{d}=-3.5$ $s_d^2=21$

1. a. Determine the values of z for which the null hypothesis. μ₁ – μ₂ = 0, would be rejected in favor of the alternative hypothesis, μ₁ – μ₂ < 0. Use α = .10.
2. b. Conduct the paired difference test described in part a. Draw the appropriate conclusions.
3. c. What assumptions are necessary so that the paired difference test will be valid? d Find a 90% confidence interval for the mean difference μ_d.
4. d. Which of the two inferential procedures, the confidence interval of part d or the test of hypothesis of part b. provides more information about the differences between the population means?