Refer to the JOM (Jan. 2003) study of a new high-strength aluminum alloy for use in antisubmarine

Question:

Refer to the JOM (Jan. 2003) study of a new high-strength aluminum alloy for use in antisubmarine aircraft, tankers, and long-range bombers, Exercise 7.43. Recall that the new alloy is obtained by applying a retrogression and re aging (RAA) heat treatment to the current strongest aluminum alloy. Strength tests conducted on three specimens of the new RAA alloy and three specimens of the current strongest alloy yielded the yield strength results (measured in megapascals, MPa) shown in the table.

a. Give the linear model appropriate for analyzing the data using regression.

b. Fit the model, part a, to the data and conduct the analysis. Summarize the results in an ANOVA table.

c. Calculate MST for the data using the ANOVA formulas. What type of variability is measured by this quantity? Does this value agree with MST in the ANOVA table, part b?

d. Calculate MSE for the data using the ANOVA formulas. What type of variability is measured by this quantity? Does this value agree with MSE in the ANOVA table, part b?

e. How many degrees of freedom are associated with MST?

f. How many degrees of freedom are associated with MSE?

g. Compute the test statistic appropriate for testing H_o: μ₁ = μ₂ against the alternative that the two treatment means differ, using a significance level of α = .05.

h. Specify the rejection region, using a significance level of α = .05.

i. State the proper conclusion in the words of the problem.

j. Use the independent samples Student’s T test of Section 8.7 to test H_o: μ₁ = μ₂ against the alternative hypothesis H_a: μ₁ ≠ μ₂. Test using α = .05.

k. It can be shown (proof omitted) that an F statistic with v₁ = 1 numerator degree of freedom and v₂ denominator degrees of freedom is equal to T², where T is a Student’s statistic based on v₂ degrees of freedom. Square the value of T calculated in part j, and show that it is equal to the value of F calculated in part g.

l. Is the analysis of variance F test for comparing two population means a one- or a two-tailed test of ? Although the T test can be used to test for either H_a: μ₁ > μ₂ or H_a: μ₁ < μ₂, the alternative hypothesis for the F test is H_a: The two means are different.

Data from Exercise 7.43

Mechanical engineers have developed a new high-strength aluminum alloy for use in antisubmarine aircraft, tankers, and long-range bombers. (JOM, Jan. 2003.) The new alloy is obtained by applying a retrogression and re aging (RAA) heat treatment to the current strongest aluminum alloy. A series of strength tests were conducted to compare the new RAA alloy to the current strongest alloy. Three specimens of each type of aluminum alloy were produced and the yield strength (measured in mega-pascals, MPa) of each specimen determined. The results are summarized in the table.