Practice Exam Questions and Solutionsfor Chapters 6, 7, 12, 15, 16, 8 and 13Statistics 301, Professor WardropChapter 61. A random sample of size n = 452 yields 113successes. Calculate the 95% confidence inter-val for p.2. A random sample of size n = 600 yields 228successes. Calculate the 98% confidence inter-val for p.3. George enjoys throwing horse shoes. Last weekhe tossed 150 shoes and obtained 36 ringers.(Ringers are good.) Next week he plans tothrow 250 shoes. Assume that George’s tossessatisfy the assumptions of Bernoulli trials.(a) Calculate the point prediction of the num-ber of ringers that George will obtain nextweek.(b) Calculate the 90% prediction interval forthe number of ringers George will obtainnext week.(c) It turns out that next week George obtains62 ringers. Given this information, com-ment on your answers in parts (a) and (b).4. Sally enjoys playing Diet-Rite-Pong. Last weekshe performed 100 trials and obtained 32 suc-cesses. Next week she plans to perform 350trials. Assume that Sally’s trials satisfy the as-sumptions of Bernoulli trials.(a) Calculate the point prediction of the num-ber of successes that Sally will obtain nextweek.(b) Calculate the 80% prediction interval forthe number of successes Sally will obtainnext week.(c) It turns out that next week Sally obtains125 successes. Given this information,comment on your answers in parts (a) and(b).5. Carl selects one random sample from a popu-lation and calculates three confidence intervalsfor p. His intervals are below.A B Cˆp ± 0.080 ˆp ± 0.040 ˆp ± 0.072Match each confidence interval to its level, withlevels chosen from: 80%, 90%, 95%, 98%, and99%. Note: Clearly, two of these levels will notbe used.6. Enid selects one random sample from a popu-lation and calculates three confidence intervalsfor p. Her intervals are below.A B Cˆp ± 0.0201 ˆp ± 0.0308 ˆp ± 0.0365Match each confidence interval to its level, withlevels chosen from: 80%, 90%, 95%, 98%, and99%. Note: Clearly, two of these levels will notbe used.Chapter 77. An observational study yields the following“collapsed table.”Group S F Total1 72 228 3002 88 212 300Total 160 440 600Below are two component tables for these data.Complete these tables so that Simpson’s Para-dox is occurring or explain why Simpson’sParadox cannot occur for these data. For thelatter, you must provide computations that jus-tify your answer.Subgp A Subgp BGp S F TotGp S F Tot1 30 30 60 1 42 198 2402 1202 180Tot 180 Tot 42018. An observational study yields the following“collapsed table.”Group S F Total1 100 100 2002 156 244 400Total 256 344 600Below are two component tables for these data.Complete these tables so that Simpson’s Para-dox is occurring or explain why Simpson’sParadox cannot occur for these data. For thelatter, you must provide computations that jus-tify your answer.Subgp A Subgp BGp S F TotGp S F Tot1 70 30 100 1 30 70 1002 802 320Tot 180 Tot 4209. An observational study yields the following col-lapsed table.Group S F Total1 41 59 1002 35 65 100Total 76 124 200Below are two component tables for these data.Complete these tables so that Simpson’s Para-dox is occurring or explain why Simpson’sParadox cannot occur for these data. For thelatter, you must provide computations that jus-tify your answer.Subgp A Subgp BGp S F TotGp S F Tot1 5 15 20 1 36 44 802 402 60Tot 60 Tot 14010. An observational study yields the following col-lapsed table.Group S F Total1 100 150 2502 42 58 100Total 142 208 350Below are two component tables for these data.Complete these tables so that Simpson’s Para-dox is occurring or explain why Simpson’sParadox cannot occur for these data. For thelatter, you must provide computations that jus-tify your answer.Subgp A Subgp BGp S F TotGp S F Tot1 57 93 150 1 43 57 1002 602 40Tot 210 Tot 14011. In a ‘Chapter 7’ problem, you are given the fol-lowing information:sˆp1ˆq1n1= 0.025, andˆp2ˆq2n2= 0.005.Calculate the half-width of the 90% confidenceinterval for p1− p2.12. In a ‘Chapter 7’ problem, you are given the fol-lowing information:1.96sˆp1ˆq1n1= 0.0679, and1.645sˆp2ˆq2n2= 0.0409.Calculate the half-width of the 80% confidenceinterval for p1− p2.Chapter 1213. A sample of size 40 yields the following sorteddata. Note that I have deleted x(39)(the sec-ond largest number). This fact will NOT pre-vent you from answering the questions below.214.1 46.0 49.3 53.0 54.2 54.7 54.754.7 54.8 55.4 57.6 58.2 58.3 58.758.9 60.8 60.9 61.0 61.1 63.0 64.365.6 66.3 66.6 67.0 67.9 70.1 70.372.1 72.4 72.9 73.5 74.2 75.3 75.475.9 76.5 77.0 x(39)88.9(a) Construct the density scale histogramfor these data using the class inter-vals: [10, 40], [40, 50], [50, 60], [60, 75]and [75, 90].(b) Calculate the first quartile and median ofthese data.(c) Calculate the 35th and 62nd percentiles ofthese data.(d) Given that the mean of these data is 63.50and the standard deviation is 12.33, whatproportion of the data lie within one stan-dard deviation of the mean?(e) Suppose that we learn that 14.1 is a mis-print. The actual observation is 64.1. Re-calculate the mean after changing the 14.1to 64.1. Also, recalculate the first quartileand median.14. A sample of size 50 yields the following sorteddata.0.01 0.04 0.04 0.06 0.08 0.10 0.120.14 0.23 0.27 0.29 0.39 0.44 0.480.50 0.58 0.58 0.62 0.70 0.71 0.720.73 0.76 0.78 0.88 1.00 1.08 1.091.10 1.10 1.14 1.16 1.30 1.30 1.311.57 1.60 1.74 1.80 1.85 1.88 1.962.22 2.27 2.45 2.96 3.44 3.86 4.054.52Hint: For these data, ¯x = 1.20 and s = 1.09.(a) Construct the density scale histogramfor these data using the class inter-vals: [0.00, 0.50], [0.50, 1.00], [1.00, 2.00]and [2.00, 5.00].(b) Calculate the median of these data.(c) Calculate the 42nd and 77th percentiles ofthese data.(d) What proportion of these data lie withinone standard deviation of the mean?(e) Calculate Q1, Q3and the mean after delet-ing the two largest observations.Chapter 1515. Independent random samples are selected fromtwo populations. Below are the sorted data fromthe first population.362 373 399 428 476 481545 564 585 589 590 600671 694 723 724 904Hint: The mean and standard deviation of thesenumbers are 571.1 and 144.7.Below are the sorted data from the second pop-ulation.387 530 544 547 646 766786 864Hint: The mean and standard deviation of thesenumbers are 633.8 and 160.8.(a) Calculate Gosset’s 90% confidence inter-val for the mean of the first population.(b) Calculate a confidence interval for the me-dian of the