STAT303 Sec 507-10Fall 2011Exam #2Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. Please print your name above so that it can be returned to you.3. There are ONLY 17 multiple-choice questions on this exam. There is partial credit. Please mark your answersclearly. Multiple marks will be counted wrong.4. You will have 50 minutes to finish this exam.5. If you have questions, please write out what you are thinking by the question so that we can discuss it later.6. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on theexam. You must work alone.7. This exam is worth the 15% of your course grade.8. When you are finished please make sure you have marked your UIN, CORRECT section (Tuesday 11:10 is 507,12:45 is 508, 2:20 is 509, and 3:55 is 510) and FORM and 17 answers, tuck your sheets in this exam and leaveeverything on the table. Put the scantron on top, upside down.9. Good luck!1STAT303 sec 510 Exam #2, Form A Fall 20111. Arsenic occurs naturally in water, and since it is a poi-son, it must be removed from drinking water. Sinceit is impossible to remove all of it, there is a maxi-mum allowable amount. Public water systems mustbe tested regularly. What should the alternative hy-pothesis be in order to ensure that the water is safe?A. The level of arsenic is not at the maximumamount.B. The level of arsenic is above the maximumamount.C. The level of arsenic is below the maximumamount.D. The level of arsenic is at the maximum amount.E. The percent of arsenic is unacceptable1. Power plants are commonly located either near riversor near oceans so that the available water can usedfor cooling the condensers. Suppose that as part of anenvironmental impact study, a power company wantsto determine if there is a difference in average watertemperature between the discharges of the two typesof plants. What are the appropriate hypotheses?A. H0: µr≤ µovs. HA: µr> µoB. H0: µr= µovs. HA: µr6= µoC. H0: µr≥ µovs. HA: µr< µoD. H0: ¯r ≤ ¯o vs. HA: ¯r > ¯oE. H0: ¯r = ¯o vs. HA: ¯r 6= ¯o2. The hypotheses H0: µ = 350 vs HA: µ < 350 areexamined using a sample of size n = 20 with mean =345 and standard deviation = 13. What is the p-valueof this test if we assume that the data is normal?A. 0.0427B. 0.9573C. 0.10 > p-value > 0.05D. 0.20 > p-value > 0.10E. We don’t have a t-table for negative numbers, sowe can’t say.2. Assume that sample data, based on two independentsamples of size 25, give us x1= 514.5, x2= 505,s1= 23, and s2= 28.2. If we wanted to test if thetrue means are equal or not, what would be the ap-propriate conservative range of the p-value if the teststatistic value is 1.305?A. 0.20 > p-value > 0.10B. 0.10 > p-value > 0.05C. 0.15 > p-value > 0.10D. 0.30 > p-value > 0.20E. 0.20 > p-value > 0.153. Using the three confidence intervals below, what isthe correct range of the p-value if I wanted to testH0: µ = 4.5 vs. HA: µ 6= 4.5? 7.5 is C.90% (4.456, 7.004)95% (4.211, 7.248)99% (3.735, 7.725)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 determine thep-value.4. We want to test whether directed reading activitiesin the classroom help elementary school students im-prove aspects of their reading ability. A treatmentclass of 23 third-grade students participated in theseactivities for eight weeks, and a control class of 23third-graders followed the same curriculum withoutthe activities. After the eight-week period, studentsin both classes took a Degree of Reading Power (DRP)test which measures the aspects of reading abilitythat the treatment is designed to improve. Refer-ence: Moore, David S., and George P. McCabe (1989).Introduction to the Practice of Statistics. Originalsource: Schmitt, Maribeth C., The Effects on anElaborated Directed Reading Activity on the Meta-comprehension Skills of Third Graders, Ph.D. disser-tation, Purdue University, 1987. Assuming the datais normal, what type test should we use if we can as-sume that all of the data is normal? µ1is the controlgroup mean and µ2is the treatment group meanA. a 1-sample t-test testing the treatment mean isgreater than the control meanB. a 2-sample t-test testing the treatment mean isgreater than the control meanC. a paired t-test testing if the control mean minusthe treatment mean greater than 0D. a 2-sample t-test testing the control mean isgreater than the treatment meanE. a 1-sample t-test testing the control mean isgreater than the treatment mean2STAT303 sec 510 Exam #2, Form A Fall 20114. You are thinking of using a t procedure to construct a95% confidence interval for the mean of a population.You suspect the distribution of the population is notnormal and may be skewed. Which of the followingstatements is correct?A. You should not use the t procedure since thepopulation does not have a normal distribution.B. You may use the t procedure provided your sam-ple size is large, say at least 50.C. You may use the t procedure since it is robust tononnormality.D. You should use a z-test since it has more power.E. You should get a different sample that is notskewed.5. There is a question as to whether the stock marketis more or less volatile this year than it was in 2008.The volatility index for 35 randomly sampled stocksis computed for both years and the difference d isrecorded for each stock. You should test the hypothe-sesA. H0: µd= 0 vs. HA: µd6= 0B. H0:¯d = 0 vs. HA:¯d 6= 0.C. H0: µd= 0 vs. HA: µd> 0.D. H0:¯d20086=¯d2011vs. Ha:¯d2008=¯d2011.E. H0: µ20086= µ2011vs. HA: µ2008= µ2011.5. A researcher wants to know if tougher sentencing lawshave had a positive effect in terms of deterring crime.He plans to select a sample of states which have en-acted a ”3 strikes” law and compare violent crimerates before the law was enacted and two years later.Let¯d be the average difference by state, µdis the truedifference in crime rates by state, before and after, µ1is the true mean crime rates before the law was en-acted and µ2is the true mean crime rate two yearslater. The correct set of hypotheses to test are:A. H0: µd= 0 vs. HA: µd6= 0B. H0:¯d = 0 vs. HA:¯d 6= 0.C. H0: µd= 0 vs. HA: µd> 0.D. H0: µ16= µ2vs. HA: µ1> µ2E. H0: µ16= µ2vs. HA: µ1= µ2.6. When stating your conclusion for the hypothesis test,you should report includeA. the p-value of the test.B. the confidence level you used.C. the significance level you
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