STAT303 Sec 510Spring 2006Exam #3Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. Please PRINT your name in the blanks provided.3. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark your answers clearly. Multiple marks will be counted wrong.4. You will have 60 minutes to finish this exam.5. If you have questions, please write out what you are thinking on the back of the page so that we candiscuss it after I return it to you.6. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade ofzero on the exam. You must work alone.7. Good luck!1STAT303 sec 510 Exam #3, Form A Spring 20061. The owner of a construction company knowsthat the overall average time to build a deck is2.5 days. Which set of hypotheses should theowner test to determine if his current crew worksfaster than the overall average? Let µcurrentbethe true average time for his current crew andµov erallbe the true average for all crews.A. H0: µcurrent= µov erallvs. HA: µcurrent6=µov erallB. H0: µcurrent= 2.5 vs. HA: µcurrent6= 2.5C. H0: µcurrent= 2.5 vs. HA: µcurrent> 2.5D. H0: µcurrent= 2.5 vs. HA: µcurrent< 2.5E. H0: µcurrent= µov erallvs. HA: µcurrent>µov erall2. Suppose you are testing whether retaking anexam improves a s tudent’s understanding, soyou run a paired t-test on H0: µdiff= 0 vs.HA: µdiff> 0, where µdiff= second − first,is the true mean difference in exam scores. Theresulting p-value is 0.34. Which of the followingis the best interpretation of this p-value?A. 34% of the students improved their scores(and understanding).B. 34% of the time you will claim that studentsimprove when they actually don’t.C. 34% of the time you will claim students dobetter the second time when they actuallydo better on the first.D. 34% of the time you will see an improve-ment such as this, when there actually isn’tany.E. The students did 34% b e tter on the secondexam than the first, on average.3. In a study of the effectiveness of a weight-lossprograms, 50 subjects who were at least 30%overweight took part in a group support programfor 10 weeks. Private weighings determined eachsubject’s weight at the beginning of the programand 9 months after the program’s end. Whattype of test do we need to use to test the effec-tiveness of the weight-loss program?A. a pooled t-testB. two-sample z-testC. one-sample t-testD. a matched pairs testA. a two-sample t-test4. A 95% confidence interval for µ1− µ2was foundto be (1.9, 18.3). What can be concluded fromthis interval?A. At α = 0.05, we would fail to reject the nullhypothesis that the two means are equal.B. Conclude µ1and µ2are significantly differ-ent.C. Reject H0: µ16= µ2.D. There is a 95% probability that µ1and µ2are significantly different.E. Two of the above are true.5. Suppose you are testing H0: π = 0.25 vs. HA:π > 0.25. The resulting p-value is 0.306. Whatis your conclusion?A. Since the p-value, 0.306, is NOT less than0.25, we fail to reject at the 25% level andconclude that there is insufficient evidenceto say that the true proportion, π > 0.25.B. Since the p-value, 0.306, is NOT less thaneven 0.10, we fail to rejec t at the 10%level and conclude that there is insufficientevidence to say that the true proportion,π > 0.25.C. Since the p-value, 0.25, is NOT less thaneven 0.10, we fail to rejec t at the 10%level and conclude that there is insufficientevidence to say that the true proportion,π > 0.306.D. Since the p-value, 0.306, is greater than0.25, we reject and conclude that there issufficient evidence to say that the true pro-portion, π > 0.25.E. Since the significance level, α, is not given,we c annot conclude anything.6. Which of the following is true?A. The t distribution takes on only positivevalues.B. The Z distribution is used instead of the tcurve to be more conservative.C. The p-value associated with a t statistic de-pends on the sample size used.D. All of the above are true.E. Exactly two of the above are true.2STAT303 sec 510 Exam #3, Form A Spring 200690% (10.177573, 11.822427)95% (10.020018, 11.979982)99% (9.7120853, 12.287915)7. Given the confidence intervals above, what is thecorrect range of the p-value for testing H0: µ =12 vs. HA: µ 6= 12?A. p-value > 0.10B. 0.10 > p-value > 0.05C. 0.05 > p-value > 0.01D. p-value< 0.01E. You need a test statistic value to determinethe p-value8. Suppose that a very skillful weight specialistphysician claims that under his regimen 92% ofhis patients lost 5% of their excess of weight in3 months. We want to test his claim about theproportion of patients that lost 5% of their ex-tra pounds using a 10% significance level. Whichnull and alternative hypotheses are appropriate?A. H0: π = 0.05 HA: π 6= 0.05B. H0: π = 0.92 HA: π 6= 0.05C. H0: π = 0.1 HA: π 6= 0.1D. H0: π = 0.92 HA: π 6= 0.92E. None of the above are the correct set of hy-potheses.9. A new teacher at a university read an articlethat discussed a study of the amount of time (inhours) college freshman study each week. Thestudy reported that the mean study time is 7.06hours. The teacher feels that freshman at heruniversity study more than 7.06 hours per weekon average. The null and alternative hypothesesare H0: µ = 7.06 vs HA: µ > 7.06. The teacherselected a simple random sample of 15 freshmenat her university and found the observed samplemean study time to be 8.43 hours and the ob-served variance to be 18.66. Assume that studytime for freshman at her university follow a nor-mal distribution. The observed test statistic anddegrees of freedom areA. 0.317 with df = 14B. 0.019 with df = 28C. 1.23 with df = 14D. 7.56 with df 28E. None of the above are correct.10. Hospital records show that 30 out of 100 men and45 out of 110 women suffer from some form de-pression. A psychiatrist claims that more womensuffer from depression than men. What type oftest should the psychiatrist run to determine ifhe/she is correct?A. Case 6: 1 sample test of proportions, test-ing whether the true proportion of womensufferers is 0.5 or more.B. Case 9: 2 sample test of means, testingwhether the true average is the same formen and women.C. Case 11: 2 sample test of proportions,testng whether the true proportion ofwomen suffe rers is more than that of men.D. Case 3: large sample test of means, sinceboth samples are more than 30.E. There’s no need to run a test since it’s ob-vious that more women s
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