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# prelim1answerkey - Introduction to Statistics Prelim#1 PAM...

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Introduction to Statistics- Prelim #1 PAM 2100 Spring 2009 Instructor: Salam Abdus STUDENT’S NAME:______________________________________________________ SECTION NUMBER:_____________________________________________ CIRCLE YOUR ANSWERS TO THE MULTIPLE CHOICE QUESTIONS. ANSWER THE PROBLEMS IN THIS EXAMINATION. WHEN YOU START, MAKE SURE YOUR EXAM HAS 8 PROBLEMS AND 20 MULTIPLE CHOICE QUESTIONS. THE EXAM HAS 14 PAGES INCLUDING THIS COVER PAGE. THE EXAM IS OUT OF 100 POINTS. THE 8 PROBLEMS ARE WORTH 60 POINTS AND THE 20 MULTIPLE CHOICE QUESTIONS ARE WORTH 40 POINTS. ALLOCATE YOUR TIME ACCORDINGLY. YOU HAVE 2 HOURS TO COMPLETE THIS EXAM.

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DO NOT WRITE ANY NOTES OR FORMULAS ON THE FRONT OR BACK OF THE EXAM OR ON TABLE A. MAKE SURE YOU CHECK ALL YOUR FINAL ANSWERS. PROB 1_____ PROB 2______ PROB 3______ PROB 4______ PROB 5______ PROB 6_____ PROB 7______ PROB 8_______ MC________ TOTAL_________ Circle your final answers to each Problem. Problem 1 (8 points) a) Below is a stemplot of home runs hit by major league teams during a month. What is the five- number summary of this data set? ( 4 points) 2| 1 3| 5 9 4| 0 3 5| 1 2 3 5 6| 4 8 7| 5 Ans. 21 39.5 51.5 59.5 75 (1 point each for the median, the first quartile and the third quartile, .5 points each for the minimum and maximum) b) Consider a data set that includes every whole number from 1 to 23: 1, 2, 3, 4, 5, ….. ,22, 23 What is the five-number summary of this data set? ( 4 points) 2
Ans. 1 6 12 18 23 (1 point each for the median, the first quartile and the third quartile, .5 points each for the minimum and maximum) Problem 2 (8 points) a) The median of a distribution x is 12 and the standard deviation of x is 6. The variable x is linearly transformed such that x new = 4x. What is the median of x new ? What is the standard deviation of x new ? (2 points) The median of x new is 12*4= 48 The standard deviation of x new is 6*4= 24 (1 point for the median, 1 point for the standard deviation) b) The mean of a distribution x is 15 and the IQR (Inter-Quartile Range) of x is 18. The variable x is linearly transformed such that x new = x+1. What is the mean of x new ? What is the IQR of x new ? The mean of x new is 15+1= 16 The IQR of x new is 18. 3

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(1 point for the mean, 1 point for the IQR) c) The mean of a distribution x is 20 and the standard deviation of x is 5. The variable x is linearly transformed such that x new = a + bx. The mean of x new is 70 and standard deviation of x new is 15. Suppose b is a positive number. What does a equal? What does b equal? (4 points) Mean(x)=20, s.d.(x)=5. 70 ) ( = new x Mean , 15 ) .( . = new x d s , bx a x new + = Now, we know that, ) .( . * ) .( . x d s b x d s new = or, 5 * 15 b = or, 3 = b Also, ) ( * ) ( x Mean b a x Mean new + = or, 20 * 3 70 + = a or, 10 = a So the answer is a= 10 , b= 3. (Correct final answers receive full credit. However if the final answer is wrong but the formulas used were correct, give 80% credit) Problem 3 (8 points) Test scores are distributed normally, with mean μ = 530 and standard deviation σ = 110. a) What proportion of the students received score at least 500? Round your value of z up to two decimal places and then use Table A. Round your final answer up to four decimal places. ( 4 points) x=500.
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prelim1answerkey - Introduction to Statistics Prelim#1 PAM...

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