Download Midterm Exam Statistics 8: Probability and Hypothesis Testing and more Exams Statistics in PDF only on Docsity! STATISTICS 8, MIDTERM EXAM 2 NAME: KEY Seat Number: ____________ Last six digits of Student ID#: ___________________ Circle your Discussion Section: 1 2 3 4 Make sure you have 6 pages, including Table A.1 on the last page. You may use two pages of notes (both sides) and a calculator. Multiple choice questions: There are 10 questions worth 4 points each (10 x 4 pts each = 40 pts). Instructions will be given when those begin on page 4. Free response questions: Show all work. If you need extra space use the back of the page, but make sure to tell us it’s there. Total of 60 points; points for each part of each question are shown. 1. (10 pts total) The sensitivity of a medical test for a certain disease is .90 and results are independent from one patient to the next. Three people who have the disease are tested. a. (4 pts) For each person tested, what is the probability that the test does not detect the disease, i.e. is a false negative? 1 – .90 = .10 b. (6 pts) What is the probability that at least one of the tests for three people with the disease comes out negative? 1 – P(0 negative tests) = 1 – (.90)3 = 1 – .729 = .271 For use by graders: Free response points: Question 1: ________ out of 10 Question 2: ________ out of 16 Question 3: ________ out of 26 Question 4: _________ out of 8 Free response score:__________ Multiple choice score:__________ Total score: ____________ 2. (16 pts total) A new drug is being proposed for the treatment of migraine headaches. Unfortunately some users in early tests of the drug have reported mild nausea as a side effect. The FDA will not approve the drug if it thinks that more than 15% (i.e. 0.15) of the population would suffer from this side effect. In an experiment to test this side effect, 400 people who suffer from migraine headaches receive the new drug and report any adverse effects. Suppose that in fact, 20% (i.e. 0.2) of the population would have mild nausea if they were to take the drug. Let p̂ be the proportion of the sample of 400 drug users in this study who will suffer mild nausea. a. (2 pts each) Give the mean and standard deviation of the sampling distribution of p̂ . Mean = ______.20____ (This is the population proportion who would have mild nausea.) Standard deviation = (.2)(.8) .02 400 b. (4 pts) Draw a picture of the sampling distribution of p̂ , marking the mean and the intervals that cover the middle 68% and 95% of the possible values. 0.240.220.200.180.160.15 possible values of p-hat 68% Normal, Mean=0.2, StDev=0.02 Sampling distribution of p-hat 95% c. (4 pts) On your figure in Part (b) show where the proportion of 0.15 would fall and compute the z- score for this value. See graph for placement of 0.15. .15 .20 2.5 .02 z d. (4 pts) The FDA will approve the drug if fewer than 15% of those in the sample experience mild nausea. What is the probability that the FDA will approve the drug based on this study? ˆ( .15) ( 2.5) .0062P p P z (from Table A.1)
