STAT303: Secs 509-511Spring 2003Exam #2Form AInstructor: Julie Hagen Carroll1. Don’t even open this until you are told to do so.2. Be sure to mark your section number (509, 510 or 511) on the scantron!3. 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.4. You will have 60 minutes to finish this exam.5. 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.6. This exam is worth 100 points, and will constitute 25% of your final grade.7. Good luck!1STAT303: 509-511 Exam #2, Form A Spring 20031. A statistic is an unbiased estimator ifA. the original population from which the sam-ple is drawn is normal.B. the sampling distribution of the statistic isnormal.C. the mean of the sampling distribution of thestatistic is the parameter of interest.D. it has the smallest variance of all the esti-mators.E. the mean of every possible sample of size nfrom the population is µ.2. The phrase (1 − α) ∗ 100% confidence meansA. the probability of the confidence intervalNOT capturing the value of the populationparameter is α.B. for a large enough sample size n, we can be(1 − α) ∗ 100% confident of capturing thetrue value of µ.C. for a large enough sample size n, ourmethod of constructing confidence intervalswill be correct (1 − α) ∗ 100% of the time.D. the estimator X is unbiased for (1 − α) ∗100% of the possible values of X based onall possible sample of size n, provided n islarge enough.E. if we could take all possible samples ofsize n and calculate the (1 − α) ∗ 100% con-fidence interval for each sample, then ex-actly (1−α)∗100% of these intervals wouldcontain the value of the population param-eter.3. Let X4∼ N(20, 52). What is P (18 < X4< 22)?A. 0.5762B. 0.5C. 0.3108D. 0E. practically 14. Which statement agrees with P (p40> 0.30) forp40∼ N(0.25, 0.0682)?A. How likely are you to get a sample propor-tion of 30% if you take a sample of 40 froma population with mean 25%?B. How likely are you to get 30% or more ifyou sample a population of 40?C. How likely are you to get a probabilitygreater than 0.30 if you sample a popula-tion with mean 0.25 and standard deviation0.068?D. How likely are you to get a sample propor-tion of 30% or more if you take a sample of40 from a population with mean 25%?E. Math doesn’t equate to words.5. “Bee pollen is effective for combating fatigue, de-pression, cancer and colon disorders.” So says aWeb site that offers the pollen for sale. We won-der if the bee pollen really does prevent colondisorders. Which of the following would mostaccurately determine the effect of bee pollen onpreventing colon disorders?A. Take a SRS of people who have colon disor-ders and find the proportion that take beepollen.B. Take a SRS of people who take bee pollenand find the proportion that have colon dis-orders.C. Take a SRS of people who do not have colondisorders. Randomly assign half of the sam-ple to take bee pollen pills and the otherhalf to take placebos. Have both groupstake the pills regularly for five years andcompare the proportion of each group thathave colon disorders.D. Take a SRS from both the population ofpeople who take bee pollen and a SRS fromthe population of people who do not takebee pollen. Compare the proportion of peo-ple in both samples who have colon disor-ders.E. Any of the above would work.6. If we each generated 20 random samples froma population of N(4, 102). From these samples,we created 20 95% confidence intervals. If welooked at all of our confidence intervals collec-tively (there were about 400), thenA. it is plausible that only 370 of them actuallycontained 4.B. although it’s not very likely, it is plausiblethat all of them actually contained 4.C. all of them would contain 4 since we alldid the same thing and we KNOW the truemean is 4.D. 380 of them would contain 4.E. Exactly two of the statements above areplausible.2STAT303: 509-511 Exam #2, Form A Spring 20037. Suppose the true mean and standard deviationof Duracell Alkaline AA battery lifetime are 5.1hr and 1.8 hr, respectively. Those of Evereadybatteries are 4.9 hr and 2.1 hr, respectively.If D100is the sample mean of 100 Duracellsand E100is the sample mean of 100 Evereadys,what is the approximate sampling distribution ofD100− E100?A. N (0.2, 0.32)B. N (0.2, 0.2772)C. N (0.2, 0.032)D. N (0.2, 0.392)E. N (2, 3.92)8. Which of the following is true?A. The proportion of times a particular eventA occurs in many, many repetitions is ap-proximately the probability of the event A.B. As you keep repeating the same experiment,the proportion of times a particular event Aoccurs will approach the true probability ofthe event A.C. The law of large numbers says that the dis-tribution of the sample proportions will ap-proach the normal distribution as you keeprepeating the same experiment.D. All of the above are true.E. Exactly two of the above are true.9. Suppose X ∼ N (10, 142). How large of a sam-ple would you need to take to have the standarddeviation of the sample mean to be half as big?A. at least 30B. 28C. 7D. 4E. 5610. Suppose a 99% confidence interval for the truemean weight of high school girls in pounds is(102.3, 106.5). If we had measured the weightsof each of the girls in kilograms (2.2 pounds =1 kilogram) then the confidence interval for themean weight of high school girls in kilogramswould have beenA. (104.5, 106.7).B. (46.5, 48.4).C. (225.06, 234.3).D. (100.1, 104.3).E. indeterminable. We would have to regatherthe data.11. Referring to the confidence interval in the previ-ous question, a 99% confidence interval for themean weight of high school girls in pounds is(102.3, 106.5), which of the following is true?A. Approximately 99% of high school girlsweigh between 102.3 and 106.5 pounds.B. There is a 99% probability that the truemean weight of high school girls is 104.4and 99% of the time the margin of errorwill be 2.1.C. If we repeatedly sampled the weight of highschool girls, 99% of the sample means wouldbe between 102.3 and 106.5.D. If we repeatedly sampled the weight of highschool girls, 99% of the time the true meanwould be between 102.3 and 106.5.E. If we repeatedly sampled the weight of highschool girls, 99% of the time the true meanfall in the calculated interval.12. Z ∼ N (0, 12). What is ±zα/2for a 55% confi-dence interval? Find
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