ec41f10MT1_sol - Kata Bognar [email protected] Economics 41...

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Kata Bognar [email protected] Economics 41 Statistics for Economists UCLA Fall 2010 Midterm 1 - suggested solutions by Yujing Xu - Part I - Multiple Choice Questions (3 points each) 1. In statistics, a population consists of: C (a) all people living in a city (b) all students in a class (c) all subjects or objects whose characteristics are being studied (d) a selection of a limited number of elements Explanation: See definition in the handout. 2. The temperatures (in Fahrenheit) observed during seven days of summer in Los Angeles are 78, 99, 67, 91, 99, 75, and 85. The mean temperature for the summers in Los Angeles is 85 with a variance of 144. Then the z-score associated with 67 degree is: A (a) -1.5 (b) 1.5 (c) -0.125 (d) 0.125 Explanation: Recall that the z-score for observation x i is z i = x i - μ σ where μ and σ are the mean and the standard deviation of the distribution. Hence, z i = 67 - 85 144 = - 1 . 5 . 3. A box contains a few red and a few white marbles. After randomly drawing two marbles from this box, you observe their color. Which of the following is an example of a simple event? C (a) At most one marble is red. (b) At least one marble is white. (c) Both marbles are white. (d) Not more than one marble is red. Explanation: The outcome space in this experiment is { RR,RW,WW } , where ‘R’ refers to a red and ‘W’ refers to a white marble. The events described in (a), (b) and (d) occur for multiple outcomes while (c) occurs only if WW is drawn. C 4. You select one person from a group of eight males and two females. The two events a male is selected and a female is selected are: C (a) independent (b) equally likely (c) exhaustive (d) none of the above Explanation: The two events are exhaustive, a person selected is either a male or a female. The two events are exclusive, it is not possible to select a male and a female at the same time, therefore they are not independent. The probability that a male is selected is 8 / 10 while the probability that a female is selected is 2 / 10 , hence the events are not equally likely. 5. 8 P 3 is equal to C (a) 56 1
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(b) 512 (c) 336 (d) none of the above Explanation: By the permutation rule 8 P 3 = 8! 5! = 336 . 6. A company has received application from 10 candidates for a financial analyst position. One candidate stands out and the other 9 seem to be equally qualified. The manager has decided to select four of the candidates for an interview. She contacts the outstanding candidate and selects three others randomly. Then the number of total selections possible is D (a) 720 (b) 504 (c) 120 (d) 84 Explanation: Since the outstanding candidate is selected for sure, the number of total selection is equal to the number of ways in which the manager can select 3 out of 9 candidates. Here the order does not matter, so you have to use the combination rule: 9 C 3 = 9! 6!3!
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ec41f10MT1_sol - Kata Bognar [email protected] Economics 41...

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