Question

Shulman Steel Corporation makes bearings that are supplied to other companies. One of the machines makes bearings that are supposed to have a diameter of 4 inches. The bearings that have a diameter of either more or less than 4 inches are considered defective and are discarded. When working properly, the machine does not produce more than 10% of bearings that are defective. The quality control inspector selects a sample of 225 bearings each week and inspects them for the size of their diameters. Using the sample proportion, the quality control inspector tests the null hypothesis p <0.10 against the alternative hypothesis p > 0.10, where p is the proportion of bearings that are defective. He always uses a 2.5% significance level. If the null hypothesis is rejected, the machine is stopped to make any necessary adjustments. One sample of 225 bearings taken recently contained 23 defective bearings. a. Using a 2.5% significance level, will you conclude that the machine should be stopped to make necessary adjustments? We conclude that the percentage of defective bearings is 0.10, and the machine be stopped to make necessary adjustments. b. Perform the test of part a using a 2% significance level. Is your decision different from the one in part a? We Ho. The result the answer in part a.

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Answer 1

Solution:

Shulman Steel Corporation makes bearings that are supplied to other companies. One of the machines makes bearings that are supposed to have a diameter of 4 inches. The bearings that have a diameter of either more or less than 4 inches are considered defective and are discarded. When working properly, the machine does not produce more than 10% of bearings that are defective. The quality control inspector selects a sample of 22 bearings each week and inspects them for the size of their diameters. Using the sample proportion, the quality control inspector tests the null hypothesis P sU.10 against the alternative hypothesis p > 0.10, where p is the proportion of bearings that are defective. He always uses a 2.570 significance level. If the null hypothesis is rejected, the machine is stopped to make any necessary adjustments. One sample of 225 bearings taken recently contained 23 defective bearings. Þ= 23 = 0,1022 a. Using a 2.5% significance level, will you conclude that the machine should be stopped to make necessary adjustments? Should not We conclude that the percentage of defective bearings is less than 0.10, and the machine be stopped to make necessary or not greater than adjustments. - Ø-p 0.1022 -0.10 = 0.11 p(1-p) 20.10(1 – 0.10) Vn V 225 p-value = P(Z > 0.11) Using the standard normal table, we have: p-value=P(Z >0.11)= 0.4558 b. Perform the test of part a using a 27 significance level. Is your decision different from the one in part a? is same as fail to reject We Ho. The result the answer in part a.