In a manufacturing facility producing fasteners,a foreman suspects that the diameter of the bolts produced by his first-shift workers is greater than the diameter of the bolts produced by his second-shift workers.He takes a sample of 5 bolts from the first shift and a sample of 4 bolts from the second shift and measures the diameters in inches.Below are the results from 5 first shift and 4 second-shift observations.The bolt diameter measurements are not normally distributed. $$\begin{array} { c c } & { \text { Bolt Diameter (inches) } } \ \text { 1st shift } & \text { 2nd shift } \ 2.01 & 1.80 \ 2.25 & 1.95 \ 1.98 & 2.30 \ 2.05 & 2.00 \ 2.03 & \end{array}$$ At ? = .05,can we conclude that his suspicion is correct? A)Reject the null hypothesis,the diameter is greater for 1^st shift versus 2^nd shift. B)Do not reject the null hypothesis,there is no evidence that the diameters differ by shift. $$\begin{array} { c c } { \text { Bolt Diameter (inches) } } \ \text { 1st shift } & \text { 2nd shift } \ 2.01 & 1.80 \ 2.25 & 1.95 \ 1.98 & 2.30 \ 2.05 & 2.00 \ 2.03 & \end{array}$$

Question

Quizplus · Accepted Answer

Since the bolt diameter measurements are not normally distributed, we cannot use a t-test. Instead, we can use a non-parametric test such as the Wilcoxon rank-sum test. We can compare the ranks of the observations from the two shifts, and if the first shift has consistently higher ranks (i.e. larger diameters), then we can reject the null hypothesis. However, after ranking the observations, we find that the sum of the ranks for the first shift is 22 and the sum of the ranks for the second shift is 25. This indicates that the second shift actually has higher ranks (i.e. larger diameters) on average. Using the Wilcoxon rank-sum test with a significance level of α = 0.05, we fail to reject the null hypothesis that there is no difference in bolt diameter between the two shifts. Therefore, the correct answer is B: Do not reject the null hypothesis, there is no evidence that the diameters differ by shift.

In a Manufacturing Facility Producing Fasteners,a Foreman Suspects That the Diameter