mid02_sol_JM - ISyE2028A,Fall2010 ThursdayNovember4...

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ISyE2028A, Fall 2010 Thursday November 4 Midterm 2 Solutions Version A 1. Which of the following statement is not always true? A. A point estimator ˆ is said to be an unbiased estimator of parameter if ˆ () E for every possible value of . B. If the estimator ˆ is not unbiased of parameter , the difference ˆ E is called the bias of ˆ . C. A point estimator ˆ is unbiased if its probability sampling distribution is always “centered” at the true value of the parameter , where “centered” here means that the median of the distribution of ˆ is . ANSWER: C 2. Which of the following statement is not true? A. Maximizing the likelihood function gives the parameter values for which the observed sample is most likely to have been generated ‐‐‐ that is, the parameter values that “agree most likely” with the observed data. B. Different principles of estimation may yield different estimators of the unknown parameters. C. The maximum likelihood estimator of the population standard deviation is the sample standard deviation S . ANSWER: C 3. Which of the following statement is not true? A. Provided that the sample size n is large, the standardized variable / ( / ) Z Xn   is approximately normally distributed, while the variable / ( / ) Z XS n is not. B. The formula /2 / x zs n  is a large sample confidence interval for with confidence level approximately 100(1 )% . C. Generally speaking, n >40 will be sufficient to justify the use of the formula / x n as a large sample confidence interval for . ANSWER: A 4. Which of the following statement is false about the chi squared distribution with degrees of freedom? A. It is a discrete probability distribution with a single parameter . B. It is positively skewed (long upper tail) C. It becomes more symmetric as increases. ANSWER: A 5. Which of the following statements are not true for any significance level? A. The one tailed rejection region zz has type I error probability . B. The one tailed rejection region ݖ൑െݖ has type I error probability . C. The two tailed rejection region or z z   has type I error probability , since area is captured under each of the tow tails of the z curve. ANSWER: C 6. In testing 12 1 2 : 0 versus : 0, where and oa H pp Hpp p p   denote the two population proportions, the value of the test statistic is found to be z = 1.82. Then, the P value is A. .9312 B. .4656 C. .0688 D. .0344 E. .9656 ANSWER: E 7. The number of degrees of freedom for a paired t test, where the data consists of 10 independent pairs, is equal to A. 20 B. 18 C. 10 D. 9
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ISyE2028A, Fall 2010 Thursday November 4 E. 8 ANSWER: D 8. Suppose that when data from an experiment was analyzed, the P value for testing :5 0 v e r s u s 0 oa HH  was calculated as .0244. Which of the following statement is true?
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This note was uploaded on 11/16/2010 for the course ISYE 2028 taught by Professor Shim during the Fall '07 term at Georgia Institute of Technology.

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mid02_sol_JM - ISyE2028A,Fall2010 ThursdayNovember4...

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