STAT303 Sec 508-510Fall 2009Exam #2Form 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 #2, Form A Fall 20091. What are the z critical values, the zα/2, for a 97% con-fidence interval?A. ±1.88B. ±1.04C. ±2.17D. ±2.97E. ±0.83402. Suppose we have a 97% confidence interval for µ =(6.93, 11.45). How do we interpret this?A. 97% of the time, the true mean will be between6.93 and 11.45.B. 97% of the time, the true mean will be 9.19.C. We are 97% confident that the true mean is be-tween 6.93 and 11.45.D. We have a 97% chance that the true mean is be-tween 6.93 and 11.45.E. Two of the above are correct interpretations.3. What is the 90th percentile of p40∼ N(0.5, 0.0792)?A. 0.5 + 1.645 ∗ 0.079B. 0.5 + 1.28 ∗ 0.079C. 0.5 + 0.90 ∗ 0.079D. 0.5 ∗ 0.90E. 0.5 ∗ 1.28 + 0.0794. Suppose we have a sample of size 40 and get a sampleproportion, p = 0.3. Do you believe that it came fromthe population above, p40∼ N(0.5, 0.0792)? Which setof hypotheses would you use to find out?A. H0: π = 0.5 vs. HA: π 6= 0.5B. H0: π ≤ 0.5 vs. HA: π > 0.5C. H0: π ≥ 0.5 vs. HA: π < 0.5D. H0: π 6= 0.5 vs. HA: π = 0.5E. H0: π < 0.5 vs. HA: π ≥ 0.55. What is the value of the test statistic, using p = 0.3,and p-value for testing H0: π = 0.5 vs. HA: π 6= 0.5?(don’t worry, I just picked the first one listed above)A. -2.76 and 0.0029B. -2.53 and 0.0057C. -2.76 and 0.0058D. -2.53 and 0.0114E. -0.2 and 0.84146. If your p-value was 0.063 (again, it doesn’t relate tothe answers above), what conclusion should we maketo the question, ‘Do you believe that it came from thepopulation above, p40∼ N(0.5, 0.0792)?’?A. Yes, of course, that’s the population we sampled.B. At the 10% level of significance, we would concludethat the true proportion, π, of our sample is not0.5.C. At the 10% level of significance, we could not con-clude that the true proportion, π, of our sample is0.5.D. At the 5% level of significance, we would not con-clude that the true proportion, π, of our sample0.5.E. Two of the above are correct conclusions.7. The larger the sample size, n, theA. less chance there is of bias in the sampling distri-bution.B. the smaller the spread of the sampling distribu-tion.C. the more likely the sampling distribution is nor-mal.D. All of the above are true.E. Only two of the above are true.8. Let’s play a game. It costs you $5 to play and most ofthe time, 55%, you don’t win anything (lose your $5),25% of the time you get your $5 back (break even), 18%of the time you win $10 (gain $5), and sometimes (???)you win $15 (gain $10). How likely are you to gain $10and what is your expected winnings? Should you playthe game?X | -5 | 0 | 5 | 10 |-------------------------------------------p(X) | 0.55 | 0.25 | 0.18 | ??? |A. 0.05, $5, sure, I’d win $5 on averageB. 0.05, $-1.35, nope, I’d lose money on averageC. 0.02, $-5, nope, I’d lose money on averageD. 0.02, $5, sure I’d win $5 on averageE. 0.02, $-1.65, nope, I’d lose money on average9. Playing the game above, how likely are you to gain $5(win $10 minus your $5 for playing) four times in a row?A. neverB. 0.001C. 0.0324D. 0.18E. 0.722STAT303 sec 508-510 Exam #2, Form A Fall 200910. If we each generated 200 random samples from a pop-ulation of N(30, 52) and created 200 95% confidenceintervals, which of the following would be true?A. Since we know the true mean is 30, all of the in-tervals would contain 30.B. Since we know the true mean is 30, exactly 95%,190, of the intervals would contain 30.C. Approximately 95% of the intervals would containthe true mean, but we can’t say what it is, i.e., wedon’t know µ.D. Both A and B are possible for a set of 200 intervalsfrom this population.E. None of the statements above are true.11. A hypothesis test, H0: µ = µ0vs. HA: µ 6= µ0wasrejected at α = 0.05. We can also sayA. the same test would be rejected at the 10% level.B. the same test would not be rejected at the 1%level.C. the greater than test, HA: µ > µ0, would also berejected at the 5% level since the p-value would behalf as large.D. All of the above are correct.E. Only two of the above are correct.12. If X ∼ N(10, 32), how likely will an average of 9 be lessthan 8?A. The sample size is too small for us to use the nor-mal distribution, so we can’t say.B. 0.0228C. 0.6667D. 0.7486E. 0.251413. Which of the following statements is correct?A. The p-value measures the probability that the nullhypothesis is true.B. The p-value measures the probability of making aType I error.C. The larger the p-value, the stronger the evidenceis against the null hypothesis.D. The smaller the p-value, the more the data dis-agrees with the hypothesized mean.E. Two of the above statements are true.14. Z ∼ N (0, 12). What is P (−0.82 < Z < 0.82)?A. 0.7939B. 0.2061C. 0.4122D. 0.3817E. 0.587815. Suppose X20∼ N(50, 62). Which of the following bestdescribes P (X20> 60)?A. how likely we are to get a sample mean based on asample of size 20 that is normal with µ = 50 andσ = 6/√20B. how likely we are to get a sample mean based ona sample of size 20, with µ = 50 and σ = 6/√20that is over 60C. how likely we are to get a sample mean based ona sample of size 20, with µ = 50 and σ = 6 that isover 60D. how likely we are to get a sample mean based ona sample of size 20, with µ = 50 and σ = 6/√20that is at least 60E. more than one is correct16. I want to test H0: µ = 10 vs. HA: µ 6= 10 but I’mgiven a 90% confidence interval for µ = (5.43, 9.86).What’s my conclusion?A. Since 10 is not in the 90% confidence interval, Ishould reject the
View Full Document
Unlocking...