Analysis of a random sample consisting of m = 20 specimens of cold-rolled steel to determine yield strengths resulted in

[answerhappygod]

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 =29.8 ksi. A second random sample of n = 25
two-sided galvanized steel specimens gave a sample average strength
of 𝑦 =34.7 ksi. Assuming that the two yield-strength distributions
are normal with 𝜎1= 4.0 and 𝜎2= 5.0
(suggested by a graph in the article “Zinc-Coated Sheet Steel: An
Overview,” Automotive Engr., Dec. 1984: 39–43), does the data
indicate that the corresponding true average yield strengths
𝜇1 and 𝜇2 are different? Carry out
a test at significance level 𝛼= 0.01.