MATH302 Statistics�Final Examination

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Statistics—MATH302FinalExaminationINSTRUCTIONS:This is an open-book and open note examination. You may use your textbook, notes, yourcomputer and a calculator during the examination.However, you are not to consult—in anymanner--with anyone while you complete this examination.Absolutely no collaboration ispermitted on this examination.This examination consists of this cover sheet and7consecutively numbered pages.There are25questions.Each question on this exam has the same weight—fourpoints—and thisexamination will count as20% of your final grade for the course.AFTERyou have answered all of the questions posed in this examination, you are to uploadyour answers into theFinalExamShell in the Examssection of our online course.DO NOTaccess theFinalExamShell until AFTER you have formulated your answers to all of thequestions on this examination.Remember, you will be able to access theFinalExamShellonly once.You must enter your answers into theFinalExamShell in the Examssection of our courseby11:59PMEastern Timeonthe due date noted in the course calendar and in theAnnouncements section of our online classroom.No late submissions will be accepted.

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11.A lawyer researched the average number of years served by 45 different justices on theSupreme Court. The average number of years served was 13.8 years with a standarddeviation of 7.3 years. What is the 95% confidence intervalestimatefor the average numberof years served by all Supreme Court justices?Place yourlimits,rounded to1decimalplace, in the blanks.When entering your answer into the Final Exam Shell do not use anylabels or symbols. Simply provide the numerical values. For example, 12.3would be alegitimate entry.Lower limit (first blank) = _____11.7___, Upper limit (second blank) = ___15.9____.2.Some defendants in criminal proceedings plead guilty and are sentenced without a trial,whereas others who plead innocent are subsequently found guilty and then are sentenced. Inrecent years, legal scholars have speculated as to whether sentences of those who plead guiltydiffer in severity from sentences for those who plead innocent and are subsequently judgedguilty. Consider the data given below on defendants accused of robbery, all of whom, by theway, had previous prison records.At the .01 level of significance, do these data suggest thatthe proportion of all defendants in these circumstances who plead guilty and are sent toprison differs from the proportion who are sent to prison after pleading innocent and beingfound guilty?PleaGuiltyNot GuiltyNumber judged guiltyn1= 191n2= 64Number sentenced to prisonx1= 101x2= 56Sample proportion1ˆ= .529p2ˆ= .875pA.No, because the test value-1.96 is inside the interval (-2.58, 2.58)B.No, because the test value-4.94 is outside the interval (-1.96, 1.96)C.Yes, because the test value-4.94 is outside the interval (-2.58, 2.58)D.Yes, because the test value 2.58 is inside the interval (-4.94, 4.94)Solution: C.Yes, because the test value-4.94 is outside the interval (-2.58, 2.58)3.Serum ferritin is used in diagnosing iron deficiency. In a study conductedrecentlyresearchers discovered that in a sample of 28 elderly men the sample standard deviation ofserum ferritin was52.6 mg/L. For 26 younger men the sample standard deviation was 84.2mg/L.At the .01 level of significance, do these data support the conclusion thatthe ferritindistribution in elderly men has a smaller variance than in younger men?A.No, because the test value 1.60 is less than the critical value of 2.54B.Yes, because the test value 2.56 is greater than the critical value of 2.54C.Yes, because the test value 0.390 is less than the critical value 2.54D.Yes, because the test value 2.56 is greater than the critical value 0.394

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2Solution: B.Yes, because the test value 2.56 is greater than the critical value of 2.544.The data presented in the table below resulted from an experiment in which seeds of 5differenttypes were planted and the number of seeds that germinated within 5 weeks afterplanting was recorded for each seed type. At the .01 level of significance, is the proportionof seeds that germinate dependent on the seed type?Seed TypeObserved FrequenciesGerminatedFailed to Germinate131725733387604524451019A.Yes, because the test value 16.86 is greater than the critical value of 13.28B.Yes, because the test value 16.86 is less than the critical value of 14.86C.No, because the test value 16.86 is greater than the critical value of 13.28D.No, because the test value 13.28 is less than the critical value of 16.86Solution: A.Yes, because the test value 16.86 is greater than the critical value of 13.285.A manufacturer of flashlight batteries took a sample of 13 batteries from a day’s productionand used them continuously until they failed to work. The lifelengthsof the batteries,inhours,untilthey failed were: 342, 426, 317, 545, 264, 451, 1049, 631, 512, 266, 492, 562,and 298. These data are also available in theworksheet Batteries in the Excel workbookMATH302_Final.xls.At the .05 level of significance, is there evidence to suggest that the mean lifelengthof thebatteries produced by this manufacturer is more than 400 hours?A.No, because the p-value for this test is equal to .1164B.Yes, because the test value 1.257 is less than the critical value 1.782C.No, because the test value 1.257 is greater than the critical value 1.115D.Yes, because the test value 1.257 is less than the critical value 2.179Solution: A. No, because the p-value for this test is equal to .11646.A survey of 85 families showed that 36 owned at least one DVD player. Find the 99%confidence interval estimate of the true proportion of families who own at least on DVDplayer. Place your limits,rounded to3decimal places, in the blanks. When entering youranswer into the Final Exam Shell do not use any labels or symbols other than the decimalpoint. Simply provide the numerical values. For example, 0.123would be a legitimate entry.Lower limit (first blank) = __0.285________, Upper limit (second blank) = ____0.562_____.

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