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 five bolts from the first shift and a sample of four bolts from the second shift and measures the diameters in inches. Below are the results from five first-shift and four second-shift observations. The bolt diameter measurements are not normally distributed. At α = .05, can we conclude that his suspicion is correct?
A) Reject the null hypothesis, the diameter is greater for first shift versus second shift.
B) Do not reject the null hypothesis; there is no evidence that the diameters differ by shift.

Question

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 five bolts from the first shift and a sample of four bolts from the second shift and measures the diameters in inches. Below are the results from five first-shift and four second-shift observations. The bolt diameter measurements are not normally distributed.  At α = .05, can we conclude that his suspicion is correct?
A) Reject the null hypothesis, the diameter is greater for first shift versus second shift. 
B) Do not reject the null hypothesis; there is no evidence that the diameters differ by shift.

Quizplus · Accepted Answer

Test failed to reject H₀. No, his suspicion is not correct. H₀: D₁ and D₂ are identical probability distributions, or H₀: μ_D₁≤ μ_D₂. H_A: D₁ is shifted to the right of D₂,or H_A: μ_D₁> μ_D₂. Reject H₀ if T ≤ T_L T_L = T_.05,5,4 = 13 11ead627_0a03_7a8a_93a1_6f5ab87074be_TB7056_00 T₁= 5 + 8 + 3 + 7 + 6 = 29 T₂ = 1 + 2 + 9 + 4 = 16 T = min(29, 16) = 16 16 > 13. We do not reject H₀. It appears that the diameter of the bolts is not larger in the first shift.

In a Manufacturing Facility Producing Fasteners, a Foreman Suspects That