MIE364S_Tutorial_0 - MIE 364S: Methods of Quality Control...

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MIE 364S: Methods of Quality Control and Improvement Tutorial 0 1. Cartons of grommets are rated at 40 pounds. Ten sample weights were obtained as follows: 41.7 40.6 41.0 42.5 40.4 42.4 42.7 41.2 42.6 41.5 Assume the weights are normally distributed with mean and variance 2 0.64 a) Test the null hypothesis 41 at significance level 0.01 . Construct a two-tailed critical region and calculate the p-value. What is your conclusion? b) Assuming the error of 1 pound is important to detect, find (40) and (42) c) Find the minimum sample size n such that the error of 1 pound is detected by the test in 1a) with probability 0.9 9. 2. An experiment wishes to demonstrate that, at 100 C, the coefficient of static friction of steel on steel when lubricated by a newly developed graphited oil is less than 0.13. The measurement process is assumed to be normally distributed with standard deviation 0.005 and the sample mean corresponding to a random sample of size 40 is 0.128 X a) Formulate and test the null hypothesis at significance level 0.05 . Calculate the p value and draw conclusions. b) Calculate the power of the test for 1 0.128 . c) Find the minimum sample size n such that the power of the test for 1 0.128 is 0.95 3. Pipe stock is automatically fed to a cutter to produce cuts of nominal length 8.05 feet. To test the accuracy of the equipment, 12 cuts are randomly selected and their lengths measured. a) Assuming the population of lengths is normally distributed, do the measurements (in feet) 8.08 8.02 8.04 8.04 8.02 8.05 8.02 8.03 8.07 8.01 8.03 8.07 yield the conclusion, at the 0.05 level, that the nominal mean length should be rejected? b) Estimate the p-value. 4. The mean time to repair (MTTR) a unit is the average time it takes to repair a unit that has been taken out of service. As an illustration, consider a robot paint-sprayer. Such a unit can fail for any number of reasons; however, let us suppose that the
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time to repair is normally distributed, but with unknown variance. It is claimed by the manufacturer that the MTTR is less than 3.4 hours. With a number of the units in operation, nine repair times are randomly selected and a t test is performed in an effort to demonstrate the manufacturer’s claim. The following times (in hours) are observed: 0.8 7.4 3.8 5.5 1.3 2.7 3.5 1.1 1.8 a) Determine if the manufacturer’s claim is supported at 0.05 significance level. b) Estimate the p-value. 5. The random variable X counts the number of bits in coded messages emanating from a certain source. Assuming X to be approximately normally distributed, it is desired to check the null hypothesis H 0 : 2 160000 at the 0.1 level a) Construct the appropriate two-tailed critical region and make a decision based upon the bit counts 4532 4606 3511 4201 3392 4639 4021 4722 3470 3100 4212 4165 b) Estimate the p-value.
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MIE364S_Tutorial_0 - MIE 364S: Methods of Quality Control...

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