A company that manufactures motors receives reels of

Chapter 8, Problem 13E

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A company that manufactures motors receives reels of 10,000 terminals per reel. Before using a reel of terminals, 20 terminals are randomly selected to be tested. The test is the amount of pressure needed to pull the terminal apart from its mate. This amount of pressure should continue to increase from test to test as the terminal is "roughed up." (Since this kind of testing is destructive testing, a terminal that is tested cannot be used in a motor.) Let \(W\) equal the difference of the pressures: "test No. 1 pressure" minus "test No. 2 pressure." Assume that the distribution of \(W\) is \(N\left(\mu_{W}, \sigma_{W}^{2}\right)\). We shall test the null hypothesis \(H_{0}: \mu_{W}=0\) against the alternative hypothesis \(H_{1}: \mu_{W}<0\), using 20 pairs of observations.

(a) Give the test statistic and a critical region that has a significance level of \(\alpha=0.05)\). Sketch a figure illustrating this critical region.

(b) Use the following data to calculate the value of the test statistic, and state your conclusion clearly:

(c) What would the conclusion be if \(\alpha=0.01)\)?

(d) What is the approximate \(p\)-value of this test?

Equation Transcription:

 

Text Transcription:

W  

N(mu_W, sigma_W^2)  

H_0:mu_W=0  

H_1:mu_W<0  

alpha=0.05  

alpha=0.01

p