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solprac3 - Midterm Examination # 3 Sta 113: Probability and...

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Unformatted text preview: Midterm Examination # 3 Sta 113: Probability and Statistics in Engineering Thursday, 2006 Nov. 30, 1:15 2:30 pm This is a closed-book exam so do not refer to your notes, the text, or any other books (please put them on the floor). You may use a single sheet of notes or formulas and a calculator, but materials may not be shared. A formula sheet and four blank worksheets are attached to the exam. You must show your work to get partial credit. Even correct answers will not receive full credit without justification. Please give all numerical answers to at least two correct digits or as exact fractions reduced to lowest terms . Write your solutions as clearly as possible and make sure its easy to find your answers (circle them if necessary), since you will not receive credit for work that I cannot understand or find. Good Luck! If you find a question confusing please ask me to clarify it. Cheating on exams is a breach of trust with classmates and faculty, and will not be tolerated. After completing the exam please acknowledge the Duke Honor Code with your signature below: I have neither given nor received unauthorized aid on this exam . Signature:-Print Name: 1. 2. 3. 4. 5. Total: Name: Sta 113 Problem 1 : For each problem answer true or false and state WHY. (15pts) a. If we keep the sample size fixed, the confidence interval gets wider as we decrease the confidence level. False. As you decrease the cofidence level upto = . 5 the confidence interval will get thinner. b. An -value of . 05 can be interpreted as assuming the null hypothesis being true and the corresponding rejection region for the null hy- pothesis will be incorrectly rejected 5% of the time. This is the type II error. False. This is type I error. c. All of the following are required in the hypothesis testing framework: data, a null and alternative hypothesis, a test statistic, the distribu- tion under the null hypothesis, the distribution under the alternative hypothesis. False. The distribution under the alternative is not required. d. If my sample size is small and I am in the hypothesis testing framework I should always use the t-distribution as the distribution under my null hypothesis. False. Only when the distributions are Gaussian. e. The p-value measures the probability that the hypothesis is true. False. See question (b) all statements except for the last one about type II error. Fall 2006 Page 1 of 10 Nov 30, 2006 Name: Sta 113 Problem 2 : Your job is to watch paint dry. Under certain conditions we know that the time to dry is normal, t N ( , 2 ). Our null (dull) and alternative hypothesis are H : = 85 H A : > 85 ....
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solprac3 - Midterm Examination # 3 Sta 113: Probability and...

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