Question

a) In order to compare the means of two populations (each of them is approximately normally distributed), independent random samples are selected from each population, with the following results: n1 = 12, x ̄1 = 7.6, s1 = 0.36, n2 = 17, x ̄2 = 6.5, s2 = 0.19. You are told that σ²1 = σ²2= σ². Based on the given data information, find the pooled estimate for σ²

^{b) For Question 16, you are told that} σ²1 = σ²2= σ^{2. You now are asked to use the pooled t-test to test H0 : μ1 = μ2 vs. Ha : μ1 > μ2. Find the observed value of the test statistic (df=27).}

Answer 1

Solution:

Given:

n₁ = 12, , s₁ = 0.36,

n₂ = 17, , s₂ = 0.19.

σ²₁ = σ²₂= σ²

Part a) Find the pooled estimate for σ²

Part b) Find the observed value of the test statistic