STAT303 Sec 508-510Spring 2009Exam #2Form AInstructor: Julie Hagen CarrollName:1. Don’t even open this until you are told to do so.2. There are 20 mutiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark youranswers clearly. Multiple marks will be counted wrong.3. You will have 60 minutes to finish this exam.4. 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.5. 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.6. 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.7. Good luck!1STAT303 sec 508-510 Exam #2, Form A Spring 20091. Suppose we are trying to test H0: µ = 3 vs. HA: µ 6=3, where µ is the average number of children a womanthinks a family should have. If we get a 95% confidenceinterval of (3.3,4.1). What conclusion is appropriate?A. There is significant evidence that the average num-ber of children a woman thinks a family shouldhave is 3.B. There is not significant evidence that the aver-age number of children a woman thinks a familyshould have is 3.C. There is significant evidence that the average num-ber of children a woman thinks a family shouldhave is not 3.D. There is not significant evidence that the aver-age number of children a woman thinks a familyshould have is not 3.E. None of the above.2. Which of the following is/are true statements?A. A probability is to a population what a sampleproportion is to a sample.B. A probability can help us decide whether to be-lieve a claim about a population (some value for aparameter) or not.C. We can use the normal distribution to find theprobability of any event as long as our sample islarge enough.D. All of the above are true.E. Only two of the above are true.3. Using the three confidence intervals below, what is thecorrect range of the p-value when testing H0: µ = 23vs. HA: µ 6= 23?90% (23.139, 26.861)95% (22.783, 27.127)99% (22.086, 27.914)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-value4. What are the missing probability and the mean for thedistribution below?X | 0 | 1 | 2 | 3 | 4 |--------------------------------------p(X) | 0.4 | 0.3 | 0.15 | 0.1 | ???A. Without the probability, we cannot determine themean.B. p(4) = 0.5 and µ = 1.4C. p(4) = 0.5 and µ = 2.9D. p(4) = 0.05 and µ = 1.1E. p(4) = 0.05 and µ = 1.55. Using the discrete distribution above, how likely are weto get all 1’s if we draw three times, assuming each drawis independent?A. 0.9B. 0.027C. 0.3D. 0.0003E. 0.00016. Again using the discrete distribution, how likely are weto get no more than a 2?A. 0.15B. 0.85C. 0.70D. 0.60E. 0.552STAT303 sec 508-510 Exam #2, Form A Spring 20097. We want to test H0: µ = 60 vs. HA: µ > 60. Weget a sample of 50 and find the mean to be 55.3. Froma previous study we know that the standard deviationis 12.8, what are the value of the test statistic and theresulting p-value?A. z = 2.60 and the p-value = 0.9953B. z = −2.60 and the p-value = 0.9953C. z = 2.60 and the p-value = 0.0047D. z = −2.60 and the p-value = 0.0047E. z = 2.60 and the p-value = 0.00948. Suppose we want to test H0: µ ≤ 60 vs. HA: µ >60 and the resulting p-value is 0.089. Which of thefollowing is the correct conclusion?A. We would reject at the 10% level and concludethat the true mean is more than 60.B. We would fail to reject at the 5 and 1% level andconclude that the true mean is not more than 60.C. We would fail to reject at the 5 and 1% levels andconclude that the true mean is no more than (lessthan) 60.D. A and B are correct conclusions.E. A and C are correct conclusions.9. Which of the following would be a Type I error for thetest above?A. The true mean is 50 and we conclude that it ismore than 60.B. The true mean is 70 and we conclude that it ismore than 60.C. The true mean is 70 and we fail to prove it is morethan 60.D. The true mean is 50 and we fail to prove it is morethan 60.E. The true mean is 70 and we fail to prove it is lessthan 60.10. Suppose the we are sampling family income data(skewed to the right data). If the true mean is $500per week with standard deviation $20 per week, whatis the distribution of the average of 50 families weeklyincome?A.X50∼ N(500, (20/50)2)B. X50∼ N(500, (400/50)2)C.X50∼ N(500,p400/502)D. The mean would be 500 and the standard devia-tion 8, but it wouldn’t be normal since the data isskewed.E. The mean would be 500 and the variance 8, but itwouldn’t be normal since the data is skewed.11. If X ∼ N (25, 142), how likely are we to get a samplemean from a sample of 25 that’s less than 20?A. 0.0179B. 0.9633C. 0.9821D. 0.0367E. 0.359412. Suppose a test of H0: µ = 0 vs. HA: µ 6= 0 is run withα = 0.05. The p-value of the test is 0.069. If you wereto calculate a 95% confidence interval for µ, would theresulting interval contain 0?A. No, because based on the p-value for the hypothe-sis test we would FTR the null, which means that0 is not a plausible value for µ.B. No, because based on the p-value for the hypothe-sis test we would reject the null, which means that0 is not a plausible value for µ.C. Yes, because based on the p-value for the hypothe-sis test we would FTR the null, which means that0 is a plausible value for µ.D. Yes, because based on the p-value for the hypothe-sis test we would reject the null, which means that0 is a plausible value for µ.E. There is not enough information to answer thisquestion.3STAT303 sec 508-510 Exam #2, Form A Spring 200913. As the number of observations increases (the samplesize increases),A. the sample statistic (x) gets closer to the true pa-rameter (µ).B. the distribution of the sample statistic looks morenormal.C. the sample statistic becomes less biased.D. All of the above are true.E. Only two of the three statements are true.14. Suppose we want to PROVE that girls are as good atmath as boys. Which set of hypotheses should we useif µgirlsis the true mean math score for girls and µboysis the true mean math score for boysA. H0: µgirls6= µboysvs. HA: µgirls= µboysandreject H0B. H0: µgirls= µboysvs. HA: µgirls6= µboysandfail to reject H0C. H0: µgirls= µboysvs. HA: µgirls< µboysandfail to reject H0D. Either B or
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