Question

Analysis of a random sample consisting of m = 20 specimens of cold-rolled steel to determine yield strengths resulted in a sample average strength of x bar = 29.8 ksi. A second random sample of n = 25 two-sided galvanized steel specimens gave a sample average strength of y bar= 34.7 ksi. Assuming that the two yield-strength distributions are normal with σ1 = 4.0 and σ2 = 5.0. Does the data indicate that the corresponding true average yield strengths µ1 and µ2 are different? Choose an alpha=0.05 significance level if needed for the problem.

HINT: Do NOT use the equation (X bar - Y bar) / sqrt(Sx^2/n+Sy^2/m). The standard deviation given is for the POPULATION (σ1, σ2) and not the sample (Sx, Sy). Doing so will lead to an inaccurate answer. Think about because the population standard deviation is given instead, the problem becomes simple where X bar ∼ N(µ1, (σ1^2)/m) and Y bar ∼ N(µ2, (σ2^2)/n). What is the distribution of the X bar − Y bar?

Answer 1