STAT303: Secs 508-510Fall 2002Exam #3Form AInstructor: Julie Hagen Carroll1. Don’t even open this until you are told to do so.2. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Pleasemark your answers clearly on the scantron. Multiple marks will be counted wrong.3. You will have 60 minutes to finish this exam.4. 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.5. This exam is worth 100 points, and will constitute 20% of your final grade.6. Good luck!1STAT303: Secs 508-510 Exam #3, Form A Fall 20021. An SRS of 100 postal employees found that theaverage time these employees had worked for thepostal service was x = 7 years with standarddeviation s = 2 years. Assume the distribu-tion of the time the employees have worked forthe postal service is approximately normal withmean µx. Are these data evidence that µxhaschanged from the value of 7.5 years of 20 yearsago? To determine this we test the hypothesesH0: µx= 7.5 vs. Ha: µx6= 7.5 using the one-sample t-test. The p-value is less than 0.01. Ifwe had a sample of only 25 employees, insteadof 100, with the same mean and standard devia-tion, the p-value would beA. larger.B. smaller.C. unchanged because the sample data is thesame.D. unchanged because the hypothesized meanis the same.E. indeterminable without actually recalculat-ing the test statistic.2. Referring to the previous question, suppose wewere not sure if the distribution of the time theemployees have worked for the postal service wasnormal. In which of the following circumstanceswould we NOT be safe using a t procedure inthis problem?A. The mean and median of the data are nearlybut not exactly equal.B. A histogram of the data shows moderateskewness.C. A stemplot of the data has a large outlier.D. The sample standard deviation is large.E. We have to know the distribution is normalsince the sample size is less than 30.3. Ok, suppose that the true mean starting salaryfor Aggies is $40,000 with a standard deviation of$1500 and that of t-sips is $30,000 and $2000,respectively. What is the distribution of the dif-ference in sample means based on samples of size100?A. N (10, 000, 52)B. N (10, 000, 5002)C. N (10, 000, 2502)D. N (10, 000, 25002)E. N (70, 000, 5002)4. An SRS of 100 of a certain popular model car in1993 found that 20 had a certain minor defectin the brakes. An SRS of 400 of this model carin 1994 found that 50 had the minor defect inthe brakes. Let π1and π2be the proportion ofall cars of this model in 1993 and 1994, respec-tively, that actually contain the defect. A 90%confidence interval for π1− π2is 0.075 ± 0.071.Suppose the sample of 1993 cars consisted of onlyseven cars, two of which had the minor brake de-fect. Also suppose the sample of 1994 cars con-sisted of only six cars, three of which had theminor brake defect. A 90% confidence intervalfor π1− π2is nowA. the same as for the original sample of 100and 400 cars.B. much wider than that for the original sam-ple of 100 and 400 cars.C. the same as a 99% for the original sampleof 100 and 400 cars.D. unsafe to compute using the normal distri-bution to approximate the sampling distri-bution of p1− p2.E. This cannot be answered without recalcu-lating the interval.5. Are avid readers more likely to wear glasses thanthose who read less frequently? Three hundredmen in the Korean army were selected at ran-dom and characterized as to whether they woreglasses and whether the amount of reading theydid was above average, average, or below aver-age. What type of test should we run to answerthe question?A. a χ2test for multiple proportionsB. an ANOVA F test for multiple meansC. a 2-sample t test for the mean of those wear-ing glasses vs. the mean of those who don’tD. a 2-sample z test for the proportion of thosewearing glasses vs. the proportion of thosewho don’tE. a non-parametric test since we don’t knowif the data is normal or not2STAT303: Secs 508-510 Exam #3, Form A Fall 20026. Which of the following is an example of a TypeII error in an ANOVA F test for the equality ofmeans?A. You conclude that there is a significant ef-fect when there really isn’t any.B. You fail to prove there is a significant effecteven though one exists.C. You claim the variances are all equal, butthey’re not.D. You claim you can’t run an ANOVA testbecause the variances are not all equal.E. You use a 1% α level when you should haveused a 10%.7. What is the advantage of the paired t test overthe other 2 sample t tests?A. It uses less data.B. It has less variability.C. It has more degresses of freedom.D. All of the above are true.E. Exactly two of the above are true.8. An SRS of 100 flights of a large airline (callthis airline 1) showed that 64 were on time.An SRS of 100 flights of another large airline(call this airline 2) showed that 80 were on time.Let π1and π2be the proportion of all flightsthat are on time for these two airlines. 90, 95and 99% confidence intervals for the differenceπ1− π2are: (−0.259, −0.055), (−0.279, −0.035)and (−0.317, 0.003) respectively. What is therange of the P -value for testing H0: π1= π2vs. Ha: π16= π2?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 -value9. Suppose we ran 10 hypothesis tests (using 20 dif-ferent samples of data) on the airline data like inthe problem above and found only 2 rejectionsfor the test H0: π1= π2vs. Ha: π16= π2.Which of the following is most likely the truth?A. Since we had 2 rejections we are confidentthat the two airlines don’t have the sameproportion of on time arrivals.B. Since we had only 2 rejections, these wereType I errors and there really isn’t a differ-ence in the proportions of on time arrivalsfor the two airlines.C. There is obviously some mistake since weshould always get the same conclusion.D. Ten runs is not enough to tell us if there isa difference in the two airlines’ proportionof on time arrivals.E. If we ran it ten more times, we’d have atotal of 4 rejections.10. Which of the following procedures is not robustto nonnormality?A. the one-sample t testB. the t test for matched pairsC. the two-sample t testD. the F test for comparing two populationstandard deviationsE. All of the above are robust procedures con-cerning the normal assumption.female male
View Full Document
Unlocking...