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# q03_sol - ISyE2028A Fall 2010 Solutions to Quiz 3(version...

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Unformatted text preview: ISyE2028A, Fall 2010 Solutions to Quiz 3 (version A & B) 1. Considering the confidence interval on the mean of a normal distribution with known variance, when the sample size n 10, it is found that the 99% confidence interval is [3, 5]. If the sample size is increased to n=160 and assume that the sample mean remains the same, what will be the new 99% confidence interval? ANSWER: [3.75, 4.25] 2. Considering the confidence interval on the mean of a normal distribution with known variance, when the sample size n 10, it is found that the 99% confidence interval is [7, 11]. If the sample size is increased to n=250 and assume that the sample mean remains the same, what will be the new 99% confidence interval? ANSWER: [8.6, 9.4] 3. A 99% confidence interval for the mean of a normal population when the standard deviation is known is found to be 98.6 to 118.4. If the confidence level is reduced to .95, the confidence interval for A. becomes wider B. becomes narrower C. remains unchanged D. None of the above answers are correct. ANSWER: B 4. A 95% confidence interval for the mean of a normal population when the standard deviation is known is found to be 98.6 to 118.4. If the confidence level is increased to .99, the confidence interval for E. becomes wider F. becomes narrower G. remains unchanged H. None of the above answers are correct. ANSWER: A 5. The waiting time at Trolley station follows distribution Uniform([0,a]), where a is the interarrival time of Trolleys. On a particular day, five students were surveyed regarding their waiting time at a Trolley station. The observed waiting times are: 1, 2, 3, 4, 10 minutes. What is the maximum likelihood estimate of a? ANSWER: 10. 6. The waiting time at Trolley stations follows distribution Uniform([0,a]), where a is the interarrival time of Trolleys. On a particular day, six students were surveyed regarding their waiting time at a Trolley station. The observed waiting times are: 1, 4, 9, 7, 16, 10 minutes. What is the maximum likelihood estimate of a? ANSWER: 16. [1 points for submission. 3 points for each question above. Total is 10.] ...
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