STAT303 Sec 508-510Fall 2007Exam #3Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. All graphs are on the last page which you may remove.3. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark youranswers 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 can discuss it afterI return it to you.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 CORRECT section (Tuesday 12:45 is 508, 2:20 is 509,and 3:55 is 510) and FORM and 20 answers, then turn in JUST your scantron to the correct pile for your section.9. Good luck!1STAT303 sec 508-510 Exam #3, Form A Fall 20071. Which of the following is true?A. We reject the null hypothesis at significance levelα if the p-value is larger than α.B. If the p-value is smaller than α while H0is true,then a Type I error has been made.C. If the p-value is larger than α then H0is true.D. A and B are true.E. B and C are true.2. Researchers are interested in how short-term memorydiffers for males and females. Suppose it is assumedthat two groups of 100 are selected randomly from nor-mal populations with similar variances. Each group isgiven a memory test and the number of correct answersis recorded. What test should be used if the researcherinterested in testing?A. A two-sample test of proportionsB. A one-sample t-testC. A two-sample t-testD. A pooled t-testE. A paired t-test3. Which of the following would be a Type II error for thehypothesis test above?A. failing to prove that men have shorter memoriesthan women even though women can remembermuch more than menB. failing to prove than men and women rememberthings differently even though we know they doC. failing to prove than men and women have differ-ent short-term memory abilities when they actu-ally are differentD. failing to prove than men and women have differ-ent short-term memory abilities when they actu-ally are the sameE. failing to remember whose memory is better4. Which of the following would be considered an advan-tage of the pooled t-test versus the two-sample t-test?A. If the assumption of equal population variancesis valid, then the pooled t-test will have greaterpower than the two-sample t-test.B. If the assumption of equal population variances isvalid, the two-sample t-test will always reject thenull hypothesis when the pooled test fails to reject.C. If the assumption of equal population variancesis valid, the two-sample t-test will always fail toreject the null hypothesis when the pooled testrejects.D. Two of the above are true.E. None of the above are true.5. Using the information below, what is the correct rangeof the p-value if I wanted to test H0: π = 0.275 vs.HA: π 6= 0.275?90% (0.286, 0.514)95% (0.264, 0.536)99% (0.222, 0.578)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-value6. Researchers were interested in determining whether di-etary calcium helps reduce blood pressure or not. In arandomized comparison, 54 white males were dividedat random into two groups. One group received cal-cium, the other a placebo. For each group seated sys-tolic blood pressure was measured. Since this is thefirst time such a study was done, the researchers wereunsure if the variation in each of the two groups wouldbe the same, but it’s known that blood pressure followsa normal distribution. What type of hypothesis testshould the researchers use?A. A two-sample test of proportionsB. A one-sample t-testC. A two-sample t-testD. A pooled t-testE. A paired t-test7. Which of the following would be a Type I error for theexperiment above?A. The researchers claim that calcium reduces sys-tolic blood pressure in men when actually it hasno effect.B. The researchers claim that calcium increases sys-tolic blood pressure in men when actually it hasno effect.C. The researchers claim that calcium has no effectwhen actually it does help reduce the systolicblood pressure in men.D. Researchers fail to prove that calcium reduces sys-tolic blood pressure in men when actually it doesreduce it.E. Researchers fail to prove that calcium has no effecteven though no effect exists.2STAT303 sec 508-510 Exam #3, Form A Fall 20078. A teacher believes that a new method of teachingwill improve reading ability for students in elementaryschool. A third grade class of 21 students learns by wayof the new method while a control group of 23 followscurriculum without the new method. After eight weeks,each classroom is then giving a test to measure readingability. A 95% confidence interval for the difference inthe average scores is (−0.935, 1.654). Assuming nor-mality holds so this confidence interval is valid, whichof the following conclusions can be made, if any?A. At the 5 and 1% levels, we can conclude that thenew method is better.B. At the 10% level, we can conclude that the oldmethod is better.C. Both A and B are correct conclusions.D. We cannot conclude that either method is betterwith a confidence interval.E. None of the above are valid conclusions.9. Suppose we want to test H0: π ≤ 0.75 vs. HA: π >0.75. From our sample of 30, we find 20 that fit thecriteria, i.e., our sample proportion is 0.67. What isour test statistic?A. Our test statistic is −1.01 so our p-value = 0.1562.B. Our test statistic is 1.01 so our p-value = 0.8438.C. Our test statistic is −0.93 so our p-value = 0.1762.D. Our test statistic is 0.93 so our p-value = 0.8238.E. The assumption of normality is not met, so wecan’t do a z-test.10. Again, suppose we want to test H0: π ≤ 0.75 vs. HA:π > 0.75 and get a valid p-value = 0.034. Which of thefollowing is the best conclusion?A. At the 5 and 10% levels, we can conclude that thetrue proportion is more than 0.75.B. At the 1% level, we can conclude that the trueproportion is less than or equal to 0.75.C. At the 5 and 10% levels, we can conclude that thetrue proportion is more than 0.67.D. All of the above are true.E. Only two of the above are true.11. A commonly prescribed drug on the market for re-lieving nervous tension is believed to be 60% effec-tive.
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