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Unformatted text preview: Kata Bognar firstname.lastname@example.org Economics 41 Statistics for Economists UCLA Fall 2010 Practice Problems for Midterm 2- suggested solutions - Multiple Choice Questions 1. Which of the following is an example of a discrete random variable? C (a) The weight of a randomly selected box of cookies (b) The length of a randomly selected window frame (c) The number of horses owned by a randomly selected farmer (d) The distance from home to work for a randomly selected worker Explanation: The variables in (a), (b) and (d) are continuous. 2. Sixty percent of children in a school do not have cavities. Let X be the number of children in a random sample of 20 children selected from this school who do not have cavities. The mean of the probability distribution of X is: D (a) 8 (b) 18 (c) 10 (d) none of the above Explanation: The random variable X follows a binomial distribution with parameters n = 20 and p = 0 . 6 . The mean of a binomial random variable is x = np = 20 . 6 = 12 . 3. There are N balls in an urn, they are either white or red. A sample of n balls is selected without replacement. Denote by X the number of red balls in the sample. D (a) X has a binomial distribution, regardless of the values of n and N. (b) X has a bernoulli distribution, regardless of the values of n and N. (c) X has a normal distribution, regardless of the values of n and N. (d) none of the above Explanation: The sampling is without replacement so X does not follow a binomial distribution. For n = 1, X has a bernoulli distribution but for other values of n that is not true. Finally, X is discrete so (c) cannot be the answer either. 4. For a normal distribution, the z score for the mean is always: A (a) equal to zero (b) negative (c) equal to 1 (d) positive Explanation: The z-score of an x value from a distribution with a mean and standard deviation is equal to x- . Thus the z-score of the mean is equal to - = 0 . 5. The area under the standard normal curve that lies between z = 0 and z = 1 . 97 is: B (a) 0.4713 (b) 0.4756 (c) 0.4761 1 (d) 0.4745 Explanation: P (0 < Z < 1 . 97) = P ( Z < 1 . 97)- P ( Z < 0) = 0 . 9756- . 5 = 0 . 4756 . 6. The standard deviation of the sampling distribution of the sample mean for a large sample D (a) is the sampling error (b) is larger than the population standard deviation (c) is always equal to the population standard deviation (d) decreases as the sample size increases Explanation: The standard deviation of the sample mean is x = n . 7. Thirty two percent of adults did not visit their physicians offices last year. Let X be the number of adults in a random sample of 15 adults who did not visit their physicians offices last year. The standard deviation of the probability distribution of X is approximately: D (a) 3.26(a) 3....
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This note was uploaded on 12/28/2010 for the course ECON 41 taught by Professor Guggenberger during the Fall '07 term at UCLA.
- Fall '07