Name: (please print) Email ID Section Homework 2 (non-Excel portion) Spring 2017 Due in class on Friday, February 3, 2017. Answers may be typed or handwritten. Take your answers out to at least two decimal places. Homeworks are graded on completion, not accuracy. Work must be shown on the homework to receive full credit. Credit for completion will not be awarded if adequate effort has not been shown. The grade will be on the BACK of this signature sheet page of the homework. Each homework is worth 2.5 points. So, for example, if a student gets a score of 2.5, it means that they did all the work, it does not mean the answers are all correct. In order to promote professional development of students in learning the importance of appearance and presentation of submitted work, 0.1 point will be deducted from homework scores for each the following conditions that are not met (students could lose a total of 0.6 points for not meeting these conditions): Name, email ID, and section number filled in (the deduction will be taken if even one of the spaces is not filled in) Stapled (all pages) Questions numbered and done in order (all work and answers for each question in one place) Pages in order with signature sheet on top, followed by the non-Excel, then the Excel Increased space between each question if the answers are included on the posted homework assignment Homework turned in at the student's scheduled section (if students are handing in homework at a different section, the homework must be given to the instructor separately) If you take any definitions/concepts directly from the packet, please cite the page number in the packet. Please sign (don't type) the Academic Integrity Pledge below: I, ______________________________, affirm that I have not and will not give or receive unauthorized aid on this deliverable, and I will complete this work honestly and according to the instructor's guidelines. (This signature sheet must be included as the top sheet of your stapled homework packet, even if all work is done on a separate sheet of paper.) If the pledge is not signed, the homework grade will remain a 0 until the pledge is signed. YOU MUST SHOW WORK TO GET CREDIT. 1. Four sections of an economics class have 30, 40, 60, and 120 students. Find the simple average and the weighted average. Include the units in your answer if this is an absolute measure. Sample: 30+40+60+120 = 62.5 4 Weighted: 30(30)+40(40)+60(60)+120(120) = 82 250 2. Calculate the mean absolute deviation of the following data set: 6, 10, 14, 14. The units are inches. Include the units in your answer if this is an absolute measure. Mean: 6+10+14+14 = 44 = 11 4 4 Deviations 6-11= -5 10-11= -1 14-11= 3 14-11= 3 1 Absolute Deviations 5 1 3 3 12 MAD: 12/4= 3 (Questions 1-2 can be completed after Lecture 4.) 3. Compute the population variance and standard deviation for the following data set: 3, 4, 8. The units are kilograms. Include the units in your answers if these are absolute measures. Mean: 3+4+8= 15/3 =5 Deviations 3-5= -2 4-5= -1 8-5= 3 1 Absolute Deviations2 4 1 9 14 Population Variance: 14/3= 4.667 Population Standard Deviation: 4.667= 2.160 Kilograms 4. The above data set of 3, 4, 8 is now a sample. Compute the sample variance and standard deviation. The units are still kilograms. Include the units in your answers if these are absolute measures. Mean: 3+4+8= 15/3 =5 Deviations 3-5= -2 4-5= -1 8-5= 3 1 Absolute Deviations2 4 1 9 14 Sample Variance: 14/2 = 7 Sample Standard Deviation: 7= 2.646 Kilograms (Questions 3-4 can be completed after Lecture 5.) 5. Compute the sample coefficient of variation for the following data set: 10, 25, 31. The units are dollars. Include the units if this is an absolute measure. Mean: 10+25+31= 66/3 = 22 Deviations Absolute Deviations2 10-22= -12 144 25-22= 3 9 31-22= 9 81 1 234 Sample Variance: 234/2 = 117 Sample Standard Deviation: 117= $10.82 6. Explain which of the following three test scores you would PREFER to receive and why after being standardized in relation to the rest of the class. Then explain which of the following three scores you would LEAST PREFER to receive and why after being standardized in relation to the rest of the class. Assume the scores are approximately bell-shaped and you prefer higher standardized scores to lower ones. You must show the work of your z-scores. Include the units in your answer if this is an absolute measure. Test Your Score Class Mean Class Standard Deviation 1 2 3 80 90 74 70 80 65 8 6 4 1 SD Above 78 86 69 1 SD Below 62 74 61 Z-Score (80-70)/8=1.25 (90-80)/6=1.67 (74-65)/4=2.25 I would least prefer to receive the score of 80, Test 1 because my z score is closest to the mean. I would prefer to receive the score of 74, Test 3 because my z score in the furthest to the right of the mean of all three scores/largest. (Questions 5-6 can be completed after Lecture 6.) 7. Four socks are in a drawer: two red and two blue. If a student randomly selects two socks from the drawer (one at a time with no replacement), what is the probability they will NOT be a pair? (As always, some kind of work must be shown to get credit. You may use a probability tree, math, or write a statement of your logic.) Question 7 can be completed after Lecture 7.) 8. What are the two requirements for a discrete probability distribution? 9. The probability of each event or combination of events must range from 0 to 1 and The sum of the probabilities of all possible events must equal 1. What are the two requirements for a random variable? Numerical Values Probabilities (don't have to be equal) associated with those values. (Questions 8-9 can be completed after Lecture 8.) 10. A quiz with 10 questions on it was given to a class of 20 students. Each question was worth one point. X = number of correct answers = 10, 9, 8 with frequencies f(X) = 8, 7, 5. Calculate the expected value of the quiz scores. Include the units in your answer if this is an absolute measure. 11. (10*8+9*7+8*5)/20 = 183/20 = 9.15 Calculate the variance of X for the following probability distribution. The units are years. Include the units in your answer if this is an absolute measure. X P(X ) 2 .2 4 .3 6 .5 12. Calculate the standard deviation of X for the following probability distribution. The units are years. Include the units in your answer if this is an absolute measure. X P(X ) 3 .1 5 .3 8 .6 (Questions 10-12 can be completed after Lecture 9 and will not be turned in. Students should complete the questions and check their answers with the Homework 2 Answer Key when they pick up Homework 2.)