# Mid1A.pdf - Midterm 1 Form A Spring 2018 Economics 203...

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Midterm 1 - Form A - Spring 2018 Economics 203 Instructor: Petry/McDermott Name: Before beginning the exam, please verify that you have 20 pages with 40 questions in your exam booklet. You should also have a decision-tree and formula sheet provided to you, as well as some blank pages for scratch paper. You need to turn in all of that at the end of the exam. Please fill out your last name, first name initial, UIN, Net-ID and “section”, according to the following table and based on the name of your TA and lab session time, on your bubble sheets. Codes for “Section” TA Name Discussion Day and Time Code Mauricio Arango Thursday 11:00am 001 Mauricio Arango Thursday 12:00pm 002 Vinicios Sant’ Anna Thursday 1:00pm 003 Whayoung Jung Thursday 2:00pm 004 Whayoung Jung Thursday 3:00pm 005 Whayoung Jung Thursday 4:00pm 006 Filia Arga Friday 9:00am 007 Juan Mu˜noz Friday 10:00am 008 Olgu ¨ Ozkul Friday 11:00am 009 Olgu ¨ Ozkul Friday 12:00pm 010 Olgu ¨ Ozkul Friday 1:00pm 011 Camila Henao Friday 2:00pm 012 Camila Henao Friday 3:00pm 013 Good luck! 1

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1. Suppose that the distribution of daily temperatures for Champaign during 2017 is symmetric and mound- shaped; with a mean of 62 F and a standard deviation of 30 F . Roughly, what proportion of days were above freezing (32 F )? a. 16% b. 32% c. 34% d. 68% e. 84% Solution: E. According to the Empirical Rule, we have 68% of the observations between 32 F and 92 F ( ± 1 standard deviaiton). We want to obtain the area from 32 F to the right. So, the remaining areas at the tails on both sides is 32% (1-0.68). The area to the left of 32 F is 16%, therefore the area to the right should be 84%. 2. Assuming that the null hypothesis is true, the p-value is: a. the probability of rejecting the null hypothesis b. the probability of rejecting the alternative hypothesis c. the probability of obtaining a test-statistic at least as extreme as the one obtained d. the probability of Type-I error e. the probability of Type-II error Solution: C. By definition, the p-value is the probability of obtaining a test-statistic at least as extreme as the one obtained. 3. You are told that the 95% confidence interval for the return of a stock is [-0.10; 0.16]. Which of the following could represent a 90% confidence interval for the return of this stock with the same sample data? a. [-0.07; 0.07] b. [0; 0.18] c. [-0.02; 0.16] d. [-0.12; 0.19] e. [-0.08; 0.14] Solution: E. The center of the confidence interval is 0.03 and should not change when modifying the confidence level. Since the confidence level decreases from 95% to 90%, the confidence interval should be narrower. Therefore, [-0.08; 0.14] is the only possible answer. 2
4. When preforming an analysis of variance (ANOVA) test, you obtain a test statistic of 0 . 6. Which of the following statements would be false ? a. The p-value would be larger than 0.5 b. The test statistic follows an F distribution c. At a 10% significance level you would fail to reject the null d. The test will tell which pairs of samples have different means e. The approximate center of the distribution is one Solution: D. In ANOVA, the null hypothesis is that all means are equal. The alternative hypothesis is that at least one of the means is not equal. However, the test does not identify which mean is different.

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