Statistical Inference: Type I Error, Hypothesis Testing, and Confidence Intervals - Prof. , Exams of Data Analysis & Statistical Methods

Download Statistical Inference: Type I Error, Hypothesis Testing, and Confidence Intervals - Prof. and more Exams Data Analysis & Statistical Methods in PDF only on Docsity! STAT303 Sec 508-510 Spring 2007 Exam #3 Form A Instructor: Julie Hagen Carroll October 10, 2007 1. Don’t even open this until you are told to do so. 2. Please PRINT your name in the blanks provided. 3. There are 20 multiple-choice questions on this exam, each worth 5 points. There is partial credit. Please mark your answers 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 after I 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 the exam. You must work alone. 7. This exam is worth the same as a regular exam (this may differ from section to section. 8. Good luck! 1 STAT303 sec 507 Exam #3, Makeup Spring 2007 1. Suppose that it is commonly assumed that the mean flight from College Station to Houston is 25 minutes. However, you believe that the true average is greater than this. You randomly choose 30 flights to take and record their times. The mean of your sample is 27. What would be a Type I error? A. Concluding that the mean is greater than 25 when it really is 25 minutes B. Concluding that the mean is not greater than 25 when the true mean is 24 C. Concluding that the mean is not greater than 25 when the true mean is 26 D. Concluding that the true mean is 24 when the true mean is 25 E. Two of the above are true. 2. The following are confidence intervals for 1 - 2 com- puted from the same data: 90% CI = (0.02, 0.09) 95% CI = (0.01, 0.12) 99% CI = (-0.03, 0.14) Based on the intervals above, if we were to test H0 : π1 = π2 vs. HA : π1 6= π2, what would be the corre- sponding p-value? 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. 3. An insurance company is conducting a study compar- ing the average number of accidents for females and males. The company wants to show on average females have less accidents than males to justify lower rates for females. What is the appropriate hypothesis? A. H0 : µfemale = µmale vs. HA : µfemale 6= µmale B. H0 : πfemale = πmale vs. HA : πfemale 6= πmale C. H0 : µfemale = µmale vs. HA : µfemale > µmale D. H0 : µfemale = µmale vs. HA : µfemale < µmale E. H0 : πfemale = πmale vs. HA : πfemale < πmale 4. A bank wonders whether omitting the annual credit card fee for customers who charge at least $5000 in a year would increase the amount charged on its credit card. The bank makes this offer to a simple random sample of 500 existing credit card customers. The bank then compares the amount charged this year with the amount charged last year for each of these customers. What type of test should be used to analyze this study? A. A two-sample test of proportions B. A one-sample t-test C. A two-sample t-test since the standard deviation is unknown D. A pooled t-test E. A paired t-test 5. Suppose we want to test whether the proportion of pa- tients who come down with a cold during their hospi- tal stay is the same for patients taking Echinacea every day and patients on a placebo drug. One herb company wants to prove that it lowers the rate at which patients catch a cold, so we set up the hypotheses: H0 : π1 = π2 and HA : π1 > π2, where π1 is the proportion of people taking the placebo who get a cold during their hospital stay and π2 is the proportion of people taking Echi- nacea who get a cold. The resulting p-value is 0.2171. What does that mean in context of the problem? A. The probability that Echinacea doesn’t keep you from catching a cold is 0.2171. B. The probability that we find a difference in propor- tions at least this small assuming that Echinacea doesn’t keep you from catching colds is 0.2171. C. Under repeated sampling, we would find that pa- tients taking Echinacea every day had the same rate of sickness as patients on a placebo 21.71% of the time, assuming Echinacea actually doesn’t keep you from catching a cold. D. Under repeated sampling, we would find that pa- tients taking Echinacea every day had at least this much lower rate of sickness about 21.71% of the time, assuming that Echinacea doesn’t keep you from catching a cold. E. Two of the above are true. 6. Which of the following best describes the relationship between a (1 − α) ∗ 100% confidence interval for µ1 − µ2 and a 2-sided test of hypotheses for µ1 = µ2 some value? A. There is no relationship between confidence inter- vals and hypothesis tests. B. If µ1 or µ2 fall within the confidence interval, we would reject the null. C. If µ1 or µ2 fall within the confidence interval, we would fail to reject the null. D. If the confidence interval contains 0, we would re- ject the null. E. If the confidence interval contains 0, we would fail to reject the null. 7. The purpose of pairing in an experiment is to A. make the samples independent. B. increase the degrees of freedom of the t-test so the test has more power. C. match the observations so that there is less chance of making an error. D. filter out the variability between the subjects. E. None of the above are correct. 2