STAT 509 Practice Final Solutions

# STAT 509 Practice Final Solutions - STAT 509 – Practice...

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Unformatted text preview: STAT 509 – Practice Final – Spring 2010 Name: __________________________________ Show work unless specified otherwise. Answers alone will not receive credit. Good Luck. (1) Below is a stem & leaf diagram for final exam scores from a previous semester. The data has been ordered and there are 50 scores in all. 4 8 9 5 0 4 5 6 8 9 6 0 0 0 3 4 4 6 8 7 0 0 2 2 2 3 4 6 7 9 9 8 1 2 3 4 4 4 5 6 6 6 7 8 8 9 9. 0 0 1 2 2 4 6 8 9 Draw and label the corresponding boxplot on the scale below. (5 points) Boxplot is drawn using 5 number summary: Low: 48 Q1: 50(.25) = 12.5 th position; rounded up to 13 th position => 64 Q2: 50(.50) = 25 th position; averate 25 th and 26th position => 78 Q3: 50(.75) = 37.5 th position; rounded up to 38 th position => 87 High: 99 (2) If time to failure of an electrical component follows an exponential distribution with a mean of 1000 hours: (a) What is the probability that the time to failure of the next component will be more than 750 hours? (5 points) > = - PY 750 e λt-. = e 75 0.4724 λ = 1/1000 t = 750 (b) What is the probability that the time to failure of the next 36 components will be more than 750 hours? (5 points) > PY 750 ( P Z > - ) 750 1000100036 = -1.50 P(Z > -1.50) = 1 – 0.0668 = 0.9332 (03) An arsenal contains several identical boxes of ammunition. The number of defective bullets per box has the following distribution. Y 1 2 3 P(y) 0.90 .07 0.027 0.003 What is the expected number of defective bullets per box in the arsenal? (5 points) E{Y} = 0 (0.90) + 1 (0.7) + 2 (0.027) + 3 (0.003) = 0 + 0.7 + 0.54 + 0.009 = 0.133 (04) The expected number of radioactive particles passing by a counter every 2 milliseconds is 4.9. What is the expected number of radioactive particles passing a counter over a 6 millisecond time frame? (5 points) 4.9 (3) = 14.7 (05) Below is summary output for a test of hypothesis that tests to see if two variances from independent populations can be considered equal. State your conclusions at .05 level of significance. Assume samples came from normal populations. (5 points) Two Sample Variance results: σ 2 1- variance of Pop'n 1 σ 2 2- variance of Pop'n 2...
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STAT 509 Practice Final Solutions - STAT 509 – Practice...

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