Statistics Section II Part A

STATISTICS FREE-RESPONSE QUESTIONS STATISTICS SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II score-75 Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. Two large corporations, A and B, hire many new college graduates as accountants at entry-level positions. In sla 2 At each оп, still employed at the corporation summarized in the boxplots below. The yearly salaries of the 60 employees in 2014 are s and were Corporation A Corporation B a) Centers are approx. equal... medians x $51K/year. More Spread in Corp. A... IOR: 56-4729K VS. 53-4726K for Corp.B Also, outliers for Corp. A, and overall lower valves, Corp. B is less varied & closer to the median overall, Corp B is slightly skened Corp A also had gaps b/w 6 a b) i (75thbtile) is larger for Corp A., so I hould have い ii) Corp 6 has less spre more consistent Salaries, I would be more guaranteed to know what my salary would be ble there are no extreme highs Hows like CorpA GO ON TO THE NEXT PAGE. STATISTICS FREE-RESPONSE QUESTIONS 2. To increase business, the owner of a restaurant is running a promotion in which a customer's bill can be randomly selected to receive a discount. When a customer's bill is printed, a program in the cash register randomly determines whether the a discount with a owner is concerned intended long-run receive a discount on the bill. The program was written to is, giving 20 of the bills a discount in the in program not run. program has a the The owner selected a random sample of bills and found that only 15 confidence interval for p, the proportion of bills that will All conditions for inference were met. ve a of them received discounts. A in run, is 0.15±0.06. =.15 (a) Consider the confidence interval 0.15±0.06. (i) Does the confidence interval provide convincing statistical evidence that the program is not working as intended? Justify your answer. (ii) Does the confidence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.2? Justify your answer. n=4x larger A second random sample of bills was taken that w sample 15 percent of the bills received the discount. mple. In the second (b) of for St al th le ld be used to (c) Based on the margin of error in part (b) that was obtained from the second sample, what do you conclude about whether the program is working as intended? Justify your answer. 2) ⅰ) No, ble the C. I is. 09 to. 21, and 20 lies within the intenel, so the program could be discounting 20% of bills, evidence that the program the time, You are looking for 20% claim. b) When n is 4x blk the SE 15 new Mio.E is 0.03. ar er the M.D.E. is divided by 2. This is and in is on the denominator. The n c) The CI. s now (.12.18). now below 20%, we now program is not working as Since the entire interval have evidence to suggest the it should be. کا STATISTICS FREE-RESPONSE QUESTIONS 3. A shopping mall has three automated teller machines (ATMs). Because the machines receive heavy use, they d 0 be d. ar y om v The Number o Probability 2 0 3 0.24 (a) What is th 102~3 working when the mall 1--15- .85 (b) What is th 0615) + 1(21)+2(140) + 3(.24) 1.73 opens? (c) What is th working? .24 .85 = .2824 that at least one ATM is (d) Given that ATMs tha alue of the number of m part (b)? Explain. valve mus #oen 2 3 *Gren at least ore work s prob 2471 .4706.2824 E(x)= 2.0355