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# exam091 - Stat 500 Midterm 1 – 8 October 2009 page 1 of 7...

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Unformatted text preview: Stat 500 Midterm 1 – 8 October 2009 page 1 of 7 Please put your name on the back of your answer book . Do NOT put it on the front. Thanks. Do not start until I tell you to. • The exam is closed book, closed notes. Use only the formula sheet and tables I provide today. You may use a calculator. • Write your answers in your blue book. Ask if you need a second (or third) blue book. • You have 2 hours (120 minutes) to complete the exam. Stop working when the end of the exam is announced. • Points are indicated for each question. There are 130 total points. • Important reminders: – budget your time. Some parts of each question should be easy; others may be hard. Make sure you do all parts you can. – notice that some parts do not require any computations. – show your work neatly so you can receive partial credit. • Good luck! Stat 500 Midterm 1 – 8 October 2009 page 2 of 7 1. 20 pts. The following problem is based on an engineering study comparing two methods (A or B) for one step in making a component. The response is the length of time required for that step. Thirty components were used in the study: 20 were randomly assigned to method A; the remaining 10 used method B. Here are summary data for each group. Method n i Time required Average s.d. A 20 14.65 3.20 B 10 7.34 1.62 In studies like these, the ratio between the two times is the most reasonable way to summarize the treatment effect. The investigators expect that method A will take longer. They want to know if the ratio of means (Method A / Method B) is larger than 1.5. (a) 5 pts. Is this a survey, an observational study or an experimental study? Briefly explain. (b) 5 pts. The investigators used a randomization test to test the null hypothesis that the ratio of the two means equals 1.5. The test statistic is the ratio of the two sample averages (i.e. Method A average / Method B average). Below are histograms of the randomization distribution given the H o : ratio = 1.5 and the bootstrap distribution. Below each figure are the largest 20 and smallest 20 observations in order. There are a total of 999 values in the randomization distribution and 1000 values in the bootstrap distribution. Ratio Frequency 1.0 1.5 2.0 2.5 50 100 150 200 Randomization Distribution Ratio Frequency 1.6 1.8 2.0 2.2 50 100 150 Bootstrap Distribution Stat 500 Midterm 1 – 8 October 2009 page 3 of 7 Randomization Bootstrap Smallest 20 1.002 1.051 1.051 1.056 1.065 1.533 1.535 1.541 1.543 1.551 1.080 1.081 1.095 1.098 1.098 1.552 1.558 1.564 1.568 1.576 1.102 1.103 1.105 1.107 1.111 1.578 1.582 1.583 1.586 1.586 1.128 1.133 1.136 1.138 1.141 1.589 1.594 1.600 1.605 1.605 Largest 20 2.415 2.129 2.129 2.121 2.079 2.338 2.308 2.265 2.265 2.247 2.074 2.055 2.054 2.031 2.023 2.246 2.245 2.236 2.227 2.220 2.019 2.018 2.017 2.012 1.995 2.212 2.203 2.203 2.197 2.192 1.992 1.985 1.979 1.979 1.966 2.191 2.186 2.185 2.184 2.180 What is the p-value for a one-sided randomization test of ratio = 1.5? Note: the alternativeWhat is the p-value for a one-sided randomization test of ratio = 1....
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exam091 - Stat 500 Midterm 1 – 8 October 2009 page 1 of 7...

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