Chapter 8.2, Problem 20E

Testing the Difference Between Two Means in Exercises 13–22, (a) identify the claim and state H₀ and H_a, (b) find the critical value(s) and identify the rejection region(s), (c) find the standardized test statistic t, (d) decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim. Assume the samples are random and independent, and the populations are normally distributed.

20. Tensile Strength An engineer wants to compare the tensile strengths of steel bars that are produced using a conventional method and an experimental method. (The tensile strength of a metal is a measure of its ability to resist tearing when pulled lengthwise.) To do so, the engineer randomly selects steel bars that are manufactured using each method and records the tensile strengths (in newtons per square millimeter) listed below.

Experimental Method:

Conventional Method:

At α = 0.10, can the engineer support the claim that the experimental method produces steel with a greater mean tensile strength? Assume the population variances are not equal.