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A large milling machine produces steel rods to certain specifications.The machine is considered to be running normally if the standard deviation of the diameter of the rods is at most 0.15 millimeters.The line supervisor needs to test the machine is for normal functionality.The quality inspector takes a sample of 25 rods and finds that the sample standard deviation is 0.19.
-Which of the following statements is the most accurate?
A)Reject null hypothesis at α = 0.025
B)Fail to reject null hypothesis at α ≤ 0.10
C)Reject null hypothesis at α = 0.05
D)Reject null hypothesis at α = 0.01

Question

Quizplus · Accepted Answer

The null hypothesis in this context is that the machine is running normally, which means the standard deviation of the diameter of the rods is at most 0.15 millimeters. A sample standard deviation of 0.19 millimeters is higher than the normal operational standard deviation of 0.15 millimeters. Without specific values for the test statistic and critical values, we can infer that a standard deviation significantly higher than the norm (0.19 vs. 0.15) would likely lead to rejection of the null hypothesis at a common significance level such as α = 0.05, but might not be significant enough to reject at a more stringent level like α = 0.01, or might not be conclusive at a higher level like α = 0.10. Therefore, the most accurate statement given the information and typical statistical thresholds would be to reject the null hypothesis at α = 0.05.

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