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1. 10-4. The burning rates of two different solid-fuel propel- lants used in aircrew escape systems are being studied. It is known that both propellants have approximately the same standard deviation of burning rate; that is o1 = o2 = 3 centimeters per second. Two random samples of n1 = 20 and n2 = 20 specimens are tested; the sample mean burn- ing rates are X1 = 18 centimeters per second and X2 = 24 centimeters per second. Test the hypothesis that both propellants have the same mean burning rate. Use C = 0.05. 3. 10-22. Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier 1 results in X1 = 290 and S1 = 12, while another random sample of 16 gears from the second supplier results in X2 = 321 and S2 = 22. Is there evidence to support the claim that supplier 2 pro- vides gears with higher mean impact strength? Use C = 0.05, and assume that both populations are normally dis- tributed but the variances are not equal. 4. 10-27. Two companies manufacture a rubber material in- tended for use in an automotive application. The part will be subjected to abrasive wear in the field application, so we decide to compare the material produced by each company in a test. Twenty-five samples of material from each company are tested in an abrasion test, and the amount of wear after 1000 cycles is observed. For company 1, the sample mean and standard deviation of wear are X1 = 20 milligrams/1000 cycles and s1 = 2 milligrams/1000 cycles, while for company 2 we obtain X2 = 15 milligrams/1000 cycles and S2 = 8 mil- ligrams/1000 cycles. Do the data support the claim that the two companies pro- duce material with different mean wear? Use a = 0.05, and assume each population is normally distributed but that their variances are not equal. 5. A study by Freedman, Pisani and Purves studied freshman at public universities and private universities in terms of the hours per week worked for pay. At public universities, the sample size was 225 with the average and standard deviation being 12.2 hours and 10.5 hours respectively. At private universities the sample size was 233 with the average and standard deviation being 9.2 hours and 9.9 hours respectively. Is there a difference in freshman hours worked between public and private at the 5% level?

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