10-7 SUMMARY TABLE FOR INFERENCE PROCEDURES FOR TWO SAMPLES

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10-7 SUMMARY TABLE FOR INFERENCE PROCEDURES FOR TWO SAMPLES

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The table in the end papers of the book summarizes all of the two-sample inference procedures given in this chapter. The table contains the null hypothesis statements, the test statistics, the criteria for rejection of the various alternative hypotheses, and the formulas for constructing the 100(1 )% con dence intervals.

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Supplemental Exercises

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10-68. A procurement specialist has purchased 25 resistors from vendor 1 and 35 resistors from vendor 2. Each resistor s resistance is measured with the following results: Vendor 1 96.8 99.6 99.7 99.4 98.6 100.0 99.4 101.1 99.8 100.3 99.9 97.7 99.1 98.5 101.1 98.6 99.6 98.3 103.7 101.9 101.2 98.2 97.7 101.0 98.2

Vendor 2 106.8 103.2 102.6 104.0 104.6 106.4 106.8 103.7 100.3 106.3 103.5 106.8 104.7 106.8 104.0 102.2 106.3 104.1 104.7 105.1 107.0 102.8 109.2 107.1 108.0 104.0 104.3 104.2 107.2 107.7 102.2 106.2 105.8 103.4 105.4

two different test conditions Use normal probability plots of the data to check these assumptions. (b) Find a 99% con dence interval on the difference in mean failure stress under the two different test conditions. (c) Using the con dence interval constructed in part (b), does the evidence support the claim that the rst test conditions yield higher results, on the average, than the second Explain your answer. 10-70. Consider Supplemental Exercise 10-69. (a) Construct a 95% con dence interval on the ratio of the variances, 1 2, of failure stress under the two different test conditions. (b) Use your answer in part (b) to determine whether there is a signi cant difference in variances of the two different test conditions. Explain your answer. 10-71. A liquid dietary product implies in its advertising that use of the product for one month results in an average weight loss of at least 3 pounds. Eight subjects use the product for one month, and the resulting weight loss data are reported below. Use hypothesis-testing procedures to answer the following questions. Initial Weight (lb) 165 201 195 198 155 143 150 187 Final Weight (lb) 161 195 192 193 150 141 146 183

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(a) What distributional assumption is needed to test the claim that the variance of resistance of product from vendor 1 is not signi cantly different from the variance of resistance of product from vendor 2 Perform a graphical procedure to check this assumption. (b) Perform an appropriate statistical hypothesis-testing procedure to determine whether the procurement specialist can claim that the variance of resistance of product from vendor 1 is signi cantly different from the variance of resistance of product from vendor 2. 10-69. An article in the Journal of Materials Engineering (1989, Vol. 11, No. 4, pp. 275 282) reported the results of an experiment to determine failure mechanisms for plasmasprayed thermal barrier coatings. The failure stress for one particular coating (NiCrAlZr) under two different test conditions is as follows: Failure stress ( 106 Pa) after nine 1-hour cycles: 19.8, 18.5, 17.6, 16.7, 16.7, 14.8, 15.4, 14.1, 13.6 Failure stress ( 106 Pa) after six 1-hour cycles: 14.9, 12.7, 11.9, 11.4, 10.1, 7.9 (a) What assumptions are needed to construct con dence intervals for the difference in mean failure stress under the

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(a) Do the data support the claim of the producer of the dietary product with the probability of a type I error set to 0.05 (b) Do the data support the claim of the producer of the dietary product with the probability of a type I error set to 0.01 (c) In an effort to improve sales, the producer is considering changing its claim from at least 3 pounds to at least 5 pounds. Repeat parts (a) and (b) to test this new claim. 10-72. The breaking strength of yarn supplied by two manufacturers is being investigated. We know from experience

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