Hypothesis Testing and Confidence Intervals in Statistics, Exams of Data Analysis & Statistical Methods

Download Hypothesis Testing and Confidence Intervals in Statistics and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! STAT302: Secs 102 and 103 Summer I 1999 Exam #3 Form A Instructor: Julie Hagen Carroll 1. Don’t EVEN open this until you are told to do so. 2. Be sure to mark your section number and your test form (A, B, C or D) on the scantron! 3. Sign your name where indicated on your scantron and write your section number, seat number and computer number beside it. You will get your scantrons back tomorrow in class. You may keep this exam. 4. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark your answers clearly on the scantron. Multiple marks will be counted wrong. 5. You will have 60 minutes to finish this exam. 6. If you are caught cheating or helping someone to cheat on this exam, you both will receive a grade of zero on the exam. You must work alone. 7. This exam is worth 100 points, and will constitute 20% of your final grade. 8. Good luck! 1 STAT302: 102 and 103 Exam #3 Form A Summer 1999 1. Ok, let’s say you just got a job as a lab tech, and you’re going to be doing different tests on pos- sible new drugs that your company is creating. Of course, the reason you got the job is because they know you have an excellent knowledge of how statistics works, and they’re sure you will do the job right! You need to find statistical evidence that your company’s new wonder drug actually works better than Brand X, which is the best selling product on the market today. Now Brand X claims their ’effectiveness’ rating is 8, out of a possible 10. You, however, are skeptical that this is true and decide to test their product along with yours. Let’s call yours Brand A, and let µA be your product’s true mean effectiveness rating. µX be the true mean effectiveness rating for Brand X. First of all, what hypotheses should you test? A. H0 : µA = µX vs. HA : µA 6= µX B. H0 : πA = πX vs. HA : πA 6= πX C. H0 : µA = µX vs. HA : µA > µX D. H0 : µA = 10 vs. HA : µA > 8 E. H0 : µA = 8 vs. HA : µA > 8 2. Same scenario: How are you going to go about getting the data to test your hypotheses? A. Take random samples of both drugs and give them to the first 50 people who have a headache. B. Take two random samples of people with headaches and give one group Brand A and the other Brand X. C. Take one random samples of people with headaches and give every other one Brand A and the rest Brand X. D. Take two random samples of people with headaches and give each person one tablet of each Brand. E. Take a couple of aspirin yourself because all of these people are giving you a headache! 3. Same scenario still: Let’s say you decide to test H0 : µA = µX vs. HA : µA < µX since you’ve decided to use time until the headache is gone, i.e., you’re testing which drug works faster. Knowing what you do about Type I and Type II errors, what α-level should you use in your test? Pick the answer that is most correct! A. Use α = 0.10 because you want to reject as much as possible. B. Use α = 0.01 because you want to reject as much as possible. C. Use α = 0.10 because you don’t want to claim there is insufficient evidence when your brand is really faster. D. Use α = 0.01 because you don’t want to claim there is insufficient evidence when your brand is really faster. E. Use α = 0.10 because you don’t want to claim your brand is better if it really isn’t any faster. 4. Ok, this is the output from your test of hypothe- ses. What can you conclude? (Don’t forget to use the p-value!) A. At the 5 and 10% levels, you conclude your brand gets rid of headaches faster. B. At the 1% level, you conclude your brand gets rid of headaches faster. C. At the 1% level, you conclude your brand takes longer to get rid of headaches. D. Both A. and C. are correct conclusions. E. None of the above are correct conclusions. 2 STAT302: 102 and 103 Exam #3 Form A Summer 1999 13. Looking at the graph above, what would have happened if we had gotten a sample proportion, p = 0.30, instead? A. The conclusion would have been exactly the same. B. The value of the test statistic would have increased. C. The value of the p-value would have de- creased. D. The value of the p-value would have in- creased. E. The probability of making a Type I error would have decreased. 14. Which of the following is FALSE? A. If I reject at the 5% level, I will always reject at the 10% level. B. A test of hypotheses can never prove the null to be true. C. Assuming the data is normal and we are given the population standard deviation, we use a t-test if the sample size is small. D. The simple random sample assumption is always necessary. E. All of the above statements are true; none are false. 15. We believe that more Aggies graduate with 4.0’s than those people who go to that little school in Austin. We gather random samples from both schools’ graduating classes, but we notice that A&M has many more students graduating (not surprising since who would want to go to that school!). What type hypothesis test should we run? Use your flow chart to help you decide. Assume that we take large enough samples for all of the necessary rules to hold. A. Case 11: a two-sample test of proportions using the number of graduates with 4.0 out of the total graduating within each school B. Case 8: a two-sample test for the mean number of 4.0 graduates since it make sense that the variances would be the same C. Case 9: a two-sample test for the mean number of 4.0 graduates since we don’t know that the variances are the same D. Case 3: two separate tests for the mean us- ing the average GPR for each school E. Case 6: two separate tests for the propor- tion of graduates with 4.0’s. 16. Ok, remember all those pennies we’ve been play- ing with? Why is it better to use 50 tosses and do this 10 times than only 5 tosses even if we do it 100 times? A. The sample proportion, p50, calculated for 50 tosses will be closer to π than the sample proportion, p5, for 5 tosses. B. The standard deviation for 50 tosses will be smaller than the standard deviation for 5 tosses. C. The distribution for 50 tosses will be ap- proximately normal, whereas the distribu- tion for 5 will not. D. All of the above are true. E. Exactly 2 of the above are true (excluding D.). 5 STAT302: 102 and 103 Exam #3 Form A Summer 1999 17. Which of the following is the best definition of the p-value in terms of the test represented above? A. The p-value = 0.029 says that 97.1% of the time we will get sample means of 15 or more when the true mean is only 12. B. The p-value = 0.029 says that 97.1% of the time we will get sample means of 12 or more when the true mean is only 15. C. The p-value = 0.029 says that there is a 2.9% chance that the true mean is only 15. D. The p-value = 0.029 says that there is a 2.9% chance that the true mean is greater than 12. E. The p-value = 0.029 says that 2.9% of the time we will get sample means of 15 or more when the true mean is only 12. 18. Which of the following defines the significance level of a hypothesis test, α? A. how often we make a Type I error. B. how often we reject H0. C. how often H0 is false. D. how often H0 is true. E. Exactly two of the above (excluding D.) 90% |Lower Limit = 10.177573 |Upper Limit = 11.822427 95% |Lower Limit = 10.020018 |Upper Limit = 11.979982 99% |Lower Limit = 9.7120853 |Upper Limit = 12.287915 19. We haven’t done this exactly in class, but using the chart at the bottom of the review sheet, what is the correct range of the p-value for testing H0 : µ = 10 vs. HA : µ 6= 10? A. p-value > 0.10 B. 0.10 > p-value > 0.05 C. 0.05 > p-value > 0.01 D. p-value< 0.01 E. You need a test statistic value to determine the p-value 20. What are the hypotheses being tested in the graph above? Read the title carefully! A. H0 : µ1 = µ2 vs. HA : µ1 = µ2 B. H0 : π1 − π2 = 0 vs. HA : π1 − π2 6= 0 C. H0 : µ1 = 0.42 vs. HA : µ2 = 0.59 D. H0 : π1 = 0.42 vs. HA : π2 = 0.59 E. H0 : µ1 − µ2 = 0 vs. HA : µ1 − µ2 6= 0 1C,2B,3C,4A,5C,6E,7A,8A,9D,10D,11E, 12E,13C,14C,15A,16E,17E,18A,19C,20B 6