Question

For a random sample of 50 measurements of the breaking strength of Brand A cotton threads, sample mean ¯x₁ = 210 grams, sample standard deviation s₁ = 8 grams. For Brand B, from a random sample of 50, sample mean ¯x₂ = 200 grams and sample standard deviation s₂ = 25 grams. Assume that population distributions are approximately normal with unequal variances. Answer the following questions 1 through 3.

1. What is the (estimated) standard error of difference between two sample means? That is, SE (X¯ _A − X¯ _B)?

2. Construct a 90% confidence interval for µ1 − µ2. (i) State the assumptions, (ii) show your work, and (iii) interpret the result in context of the problem.

3. Using the same samples, you want to test whether the difference between two population means is 5 grams or not at the significance level α = 0.1. H₀ : µ_A − µ_B = 5 vs H₁ : µ_A − µ_Bnot equal to 5. What would your conclusion be? Support your answer briefly. You don’t need to conduct the hypothesis test.

Answer 1