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?

Answer:

We accept H₀, we don´t have enough evidence to claim that the procedure improves the tensile strength above the peviuos average

Step-by-step explanation:

Information:

μ  = 2150

Sample size    n  = 16

Sample mean   x  =  2160

Sample standard deviation    s = 30

a) Test Hypothesis

Null Hypothesis                                    H₀         x = μ

Alternative Hypothesis                         Hₐ         x > μ

b) If Tensile strength is  approximately normal distribution we should use t-student statistic for testing the above hypothesis.

t(s) = ??    with  df = n - 1      df  =  15

c)  t(s)  =  ( x - μ ) / s/√n

t(s)  = ( 2160  -  2150 ) / 30/√16

t(s)  = 10*4 / 30

t(s) = 1,33

d) In t-student we look for p-vale for 1,33 and  df = 15

p-value = 0,1

e) If the level of significance is 0,05, then    α/2 = 0,025

we compare p-value and level of significance

p-value     0,1 > 0,025

Then p-value is bigger than the significance level, we should accept H₀

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