Construct a 90% confidence interval for μ1 − μ2. (i) State the assump- tions, (ii) show your work, and (iii) interpret the result in context of the problem. 2. Using the same samples, you want to test whether the difference between two population means is 5 or not at the significance level α = 0.1. H0 : μ1 − μ2 = 5 vs H1 : μ1 − μ2 ̸= 5. What would your conclusion be? Support your answer briefly. You don’t need to conduct the hypothesis test.
For a random sample of 50 measurements of X1, sample mean x ̄1 = 200, sample standard deviation s1 = 10. For X2, from a random sample of 50, sample mean x ̄2 = 190 and sample standard deviation s2 = 15. Assume that population distributions are approximately independent normal with unequal variances. Answer the following questions 1 through 3.
1. Construct a 90% confidence interval for μ1 − μ2. (i) State the assump- tions, (ii) show your work, and (iii) interpret the result in context of the problem.
2. Using the same samples, you want to test whether the difference between two population means is 5 or not at the significance level α = 0.1. H0 : μ1 − μ2 = 5 vs H1 : μ1 − μ2 ̸= 5. What would your conclusion be? Support your answer briefly. You don’t need to conduct the hypothesis test.
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