mt2sol - GE331/IE 300 Analytic Methods For Uncertainty /...

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GE331/IE 300 Analytic Methods For Uncertainty / Analysis of Data Spring 2011 University of Illinois G. Koksal EXAM II Thursday, April 7, 7:00-8:30 pm Open textbook, lecture notes and/or cheat sheets. Calculators are allowed. NAME: Solution Key for Type A Please clearly PRINT your name in CAPITAL LETTERS. ITEM Questions Total PART 1 (30 points) 1 2 3 4 5 6 7 8 9 10 11 12 Answers PART II (75 points) 1 2 3 4 5 Scores Total
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Name: Solution Key 4.7.2011 GE331/IE300 EXAM 1 PART I (30 points) Choose the best answer to the following questions. Circle your answers on the questions and also write them on the table on the cover sheet . 1) (2.5 pts.) Suppose a sample of size n 1 is taken from a normal distribution the population mean of which is unknown and the population variance is . If we want to decrease the length of the 100(1-  % confidence interval X 1 n z  for the mean by half then we must take a sample of size n 2 given approximately by a) n 2 = ( 1 n 2 z  ) 2 b) n 2 =2 n 1 c) n 2 =n 1 /2 d) n 2 =4 n 1 Answer: d 1 2 1 2 / 2 2 / 4 ) ( 2 1 n n n z n z 2) (2.5 pts.) Let H 0 : = 0 , H 1 : . Let X be the mean of a random sample with large n. Then, a) As X gets closer to 0 , the corresponding p-value increases. b) If H 0 is rejected, then p-value of the test statistic is greater than . c) p-value increases as increases. d) If X = 0 , then p-value is 0.5. Answer: a 3) (2.5 pts.) n S X T / 0 0 A _____ such as T 0 is called ____ , and T 0 is simply a function of ____. a) Parameter, a test statistic, population. b) Test statistic, a parameter, population. c) Random variable, the critical value, samples. d) Parameter, the critical value, random variables. e) Random variable, a test statistic, samples.
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Answer: e 4) (2.5 pts.) Suppose that you are testing a hypothesis on the variance of a normal distribution. Consider the following display: Test and CI for One Variance Null hypothesis Sigma-squared = 18 Alternative hypothesis Sigma-squared not = 18 95% Confidence Intervals CI for CI for Method StDev Variance Chi-Square (3.30, 8.76) (10.9, 76.8) Which of the following can be concluded based on this output? a) The p-value should be less than 0.05 b) The true 2 value cannot be more than 76.8 c) Reject that 2 =18 with 95% confidence d) Fail to reject that =4.2426 with 95% confidence Answer: d 5) (2.5 pts.) In a market research, customer representatives were selected based on their income levels and ages. Four groups were defined: low income-teenager, high income-teenager, low income-adult, high income-adult. In each group a certain proportion of customers were randomly selected. What type of sampling is this?
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This note was uploaded on 01/26/2012 for the course IE IE 300 taught by Professor Zafarani during the Spring '09 term at University of Illinois, Urbana Champaign.

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mt2sol - GE331/IE 300 Analytic Methods For Uncertainty /...

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