STAT303 Sec 508-510Spring 2010Exam #3Form AInstructor: Julie Hagen CarrollName:1. 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. 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 #3, Form A Spring 20101. If we sample from p50∼ N(0.25, 0.06122), how likelyare we to get a sample proportion of 30% or more?A. 0.2061B. 0.6179C. 0.7939D. 0.8170E. 0, the z-score is more than 5H0 : pi1 - pi2 = 0HA : pi1 - pi2 not equal 0Difference Sample Diff. Std. Err. Z-Stat P-valuep1 - p2 -0.22807017 0.1322165 -1.72 0.08452. The test above was to see if men (pi2) where morelikely to help someone carry their bags from the mallthan women (pi1). Which of the following is/are true?A. This should have been a 1-sample test to see ifpi2 was greater than 0.5, so we can’t answer thequestion.B. The p-value is 0.0845, so we can conclude at the10% level that proportion of men who would helpis greater than the proportion of women.C. The p-value is 0.04225, so we can conclude at the5% level that proportion of men who would helpis greater than the proportion of women.D. The p-value is 0.95775, so we cannot conclude thatproportion of men who would help is greater thanthe proportion of women.E. At the 5% level we would say the proportions arethe same.3. What is P (p150− p250< 0.20) if p150− p250∼N(0.25, 0.0252)?A. 1B. 0C. We can’t have a negative proportion, so this isimpossible.D. 0.0228E. 0.97724. What does it mean for the χ2test statistic to equal 0 inthe test for independence of two categorical variables?A. It means we would reject the null and concludethe two variables are related.B. It means we would reject the null and concludethe two variables are independent.C. It means the two variables are completely (ex-actly) dependent.D. It means the two variables are completely (ex-actly) independent.E. It means that the assumptions are not valid sincethe expected counts are 0.5. Historically, there are more boys born in the UnitedStates than girls, 51.5% of newborns are in fact boys.Does this mean that there is a significantly higher pro-portion of newborn boys than girls? What should wetest?A. H0: πb= πgvs. HA: πb6= πgB. H0: πb≤ πgvs. HA: πb> πgC. H0: πb= πgvs. HA: πb6= 0.515D. H0: πb≤ 0.515 vs. HA: πb> 0.515E. H0: πg≤ 0.515 vs. HA: πg> 0.5156. Suppose we decided to test H0: πb= 0.5 vs. HA: πb6=0.5 (not even one of the choices so don’t worry aboutyour last answer). We took a sample of 45 newbornsand found 48% of them were boys. What is the correctconclusion?A. We can’t calculate the test statistic since the stan-dard deviation isn’t given.B. The true proportion of newborn boys is 39.36%not 50%.C. The p-value = 0.7872, so we don’t have enough ev-idence to say that the true proportion of newbornboys is 0.5.D. The p-value = 0.7872, so we don’t have enough ev-idence to say that the true proportion of newbornboys is not 0.48.E. The p-value = 0.7872, so we don’t have enough ev-idence to say that the true proportion of newbornboys is not 0.5.7. Let µp150= 0.5, σp150= 0.0707 with np150= 50 andµp225= 0.75, σp225= 0.0866 with np225= 25, what isthe distribution of p150− p225if the two populationsare independent?A. Since p225is not normal, we can only sayµp150−p225= −0.25.B. Since p225is not normal, we can only sayµp150−p225= +0.25.C. p150− p225∼ N(−0.25, 0.01592)D. p150− p225∼ N(−0.25, 0.15732)E. p150− p225∼ N(−0.25, 0.01252)8. I have a 95% confidence interval for π, the true pro-portion of voters in favor of Propostion 2, (0.49, 0.56).Which of the following statements are valid based onthis interval?A. I could not reject the hypothesis that half of thepeople are in favor of Propostion 2 at the 10%level.B. I could not reject the hypothesis that half of thepeople are in favor of Propostion 2 at the 5% level.C. I could not reject the hypothesis that half of thepeople are in favor of Propostion 2 at the 1% level.D. Two of the above are correct.E. None of the above are correct.2STAT303 sec 508-510 Exam #3, Form A Spring 2010Lived Died TotalCrew 212 673 885(23.95%) (76.05%) (100.00%)First 202 123 325(62.15%) (37.85%) (100.00%)Second 118 167 285(41.4%) (58.6%) (100.00%)Third 178 528 706(25.21%) (74.79%) (100.00%)Total 710 1491 2201(32.26%) (67.74%) (100.00%)Statistic DF Value P-valueChi-square 3 187.79321 <0.00019. The table above lists the survivor count by type of pas-senger (First Class, etc.) and crew. What statisticalconclusion can be made from this data?A. The crew stayed behind to help the passengers getout safely.B. The rich (First Class passengers) were helped offfirst, so they were more likely to survive.C. The poor (Third Class passengers) were helped offlast, so they were less likely to survive.D. There is a significant relationship between type ofpassenger (including crew members) and whetherthey survived or not.E. All of the above are valid conclusions for this data.10. What is the expected count for a Second Class survivor(rounded to 0 decimals)?A. 118B. 92C. 911D. 294E. 511. What assumption needed to be true for the previoustest to be valid?A. Each expected cell count needed to be at least 30.B. Each expected cell count needed to be at least 10.C. Each expected cell count needed to be at least 5.D. The average expected cell count needed to be atleast 5.E. None of the above are right.12. Which of the following would be a Type I error in theχ2test?A. We concluded that more crew members died thanany type of passenger (First, etc.), but it’s nottrue.B. We concluded that the proportion of deaths wasdifferent for each class, but it wasn’t.C. We failed to prove that there was a relationshipbetween type of passenger and surviving.D. We concluded that the type of passenger and sur-viving were not related, but they are.E. We concluded that the type of passenger and
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