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ioe265f11-Practice+Final-2

ioe265f11-Practice+Final-2 - IOE 265 F2011 PRACTICE FINAL...

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IOE 265 F2011 PRACTICE FINAL EXAM (2) 1 of 15 Part I. Multiple Choice (10 questions, 4 points each, 40 points total) 1. If A and B are disjoint or mutually exclusive events with P ( A ) > 0 and P ( B ) > 0, then a. P = P ( A ) + P ( B ) b. P = c. P = P ( A ) + P ( B ) d. P = 2. If are three independent random variables with variances of 2, 4, and 5, respectively, then is a. 36 b. 12 c. 124 d. 140 3. How many combinations of size 2 can be constructed from the set (A, B, C, D, E, and F)? 4. The cumulative distribution function F ( x ) of a discrete random variable X is given by F (0) = 0.30, F (1) =0 .70, F (2) = 0.90, and F (3) = 1.0, then the value of the probability mass function p ( x ) at x = 1 is 5. Let X be a discrete random variable with E ( X ) = 8.6. Then E (3 X + 5.6) is 6. Which of the following is not a condition of a binomial experiment? a. There is a sequence of n identical trials. b. Each trial results in at least two outcomes. c. The trials are independent of each other. d. The probability of success p is constant from one trial to another.

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IOE 265 F2011 PRACTICE FINAL EXAM (2) 2 of 15 7. If X is a normally distributed random variable with a mean of 25 and a standard deviation of 8, then the probability that X exceeds 20 is approximately 8. Which of the following statements are true if is a random sample from a distribution with mean ? 9. If X is a nonnegative random variable and the random variable Y = LN( X ) is normally distributed with parameters, then which of the following statements are not true? 10. If P (A|B) = P (A), and P (B|A) = P (B) , then events A and B are said to be: a. independent b. mutually exclusive c. dependent d. complementary
IOE 265 F2011 PRACTICE FINAL EXAM (2) 3 of 15 Part II. Briefly answer the following questions (10 points each, 20 points total) – Do not use more than the space provided below. 11. Two chemical companies can supply a raw material. The concentration of a particular element in this material is very important. The mean concentration for both suppliers is the same, but there is suspicion that the variance in concentration is different. Minitab output of the analysis is as follows: Test for Equal Variances 95% confidence intervals for standard deviations Sample N Lower StDev Upper 1 20 1.55414 2.12132 3.28655 2 18 0.94879 1.51658 3.47369 F-Test (normal distribution) Test statistic = 1.96, p-value = 0.370 In your own words, explain what the p-value of this test means. Based on this interpretation, is there evidence to claim that supplier 2 produces batches of material more consistently (with smaller variance) than supplier 1? 12. Using the normal curves below, illustrate the areas under the curve that correspond to type I error, type II error and power (include the corresponding values for each) for the following hypothesis test: Part III. Solve the following problems. Show all your work and clearly mark your answer (5 problems, 65 points total)

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IOE 265 F2011 PRACTICE FINAL EXAM (2) 4 of 15 13. (15 points) A study of the ability of individuals to walk in a straight line reported that accompanying data on cadence (strides per seconds) for a sample of n = 20 randomly selected healthy men: .95 .81 .93 .95 .93 .86 1.05 .92 .85 .81 .92 .96 .92 1.00 .78 1.06 1.06 .96 .85 .92 A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from MINITAB follows. Variable N Mean Median StDev SEMean Cadence 20 0.9255 0.9300 0.0809 0.0181

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