Solved: One method for straightening wire before coiling

Chapter 8, Problem 60E

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Problem 60E

One method for straightening wire before coiling it to make a spring is called “roller straightening.” The article “The Effect of Roller and Spinner Wire Straightening on Coiling Performance and Wire Properties” (Springs, 1987: 27–28)reports on the tensile properties of wire. Suppose a sample of 16 wires is selected and each is tested to determine tensile strength (N/mm2). The resulting sample mean and standard deviation are 2160 and 30, respectively.

a. The mean tensile strength for springs made using spinner straightening is 2150 N/mm2. What hypotheses should be tested to determine whether the mean tensile strength for the roller method exceeds 2150?

b. Assuming that the tensile strength distribution is approximately normal, what test statistic would you use to test the hypotheses in part (a)?

c. What is the value of the test statistic for this data?

d. What is the P-value for the value of the test statistic computed in part (c)?

e. For a level .05 test, what conclusion would you reach?