Assignments:1. A. In order to discover the average number of children, Fred, a young college

professor at a large Midwestern university, conducted a survey in which a random sample of 1,000 students in Psychology 101 were asked how many children (including themselves) were in their family. The researcher added all the data together and divided by 1,000 and uncovered the answer – 3.5. The most recent census has found that the average number of children in a U.S. family is 2.5. a. Why are these two numbers different?b. Should Fred have designed his study differently to get the right

answer?c. How?

B. Prenatal screening for Down syndrome for mothers over the age or 35 is usually recommended. A non-invasive test is about 95% accurate. That is, if the fetus has Down syndrome it will be detected 95% of the time. And if the fetus does not have Down’s it will correctly say so 80% of the time. We know that Down’s is not very common, affecting only about one in every 200 fetuses whose mothers are over age 35.

a. What is the probability that if the test says the fetus has Down’s, that the test is correct?

b. What is the probability that if the test says the fetus doesn’t have Down’s, that the test is correct?

C. In a survey of hospitals it was found that those hospitals that had the highest proportion of female births tended to also have the fewest births of any of the hospitals in the survey. The Jones family, having already had a son, decided to boost their chances of a daughter by going to one of the hospitals that, so far this year, had the highest likelihood of female births.a. Is this a sensible strategy? b. If so, why? If not, why not?c. How does this shed light on why the best performing mutual funds are usually small? d. Should this guide our investment strategy? If so, why? If not, why not?

2. A. Find data displays in the mass media that illustrate at least two of the most common errors. You can find one display with multiple flaws, or two displays with one flaw apiece. Redo the displays correctly. Explain (i) where you found the displays, (ii) what you believe the point of the display was, (iii) what were the flaws, and (iv) what you did to fix them.

(e.g. see http://flowingdata.com/2009/11/26/fox-news-makes-the-best-pie-chart-ever/)

B. What were the key lessons in Arbuthnot’s (1710) paper? Compare the explanations for the change in the number of christenings in 1704 with that in 1665-1666.

B. Find one wonderful display in the mass media. Explain (i) where you found the display, (ii) what you believe the point of the display was, (iii) why you think it is wonderful.

3 A. With your knowledge of improved methods of multivariate display, develop a display the following data set:

  Antibiotic  

Bacteria Penicillin Streptomycin NeomycinGram

StainingAerobacter aerogenes 870 1 1.6 negativeBrucella abortus 1 2 0.02 negativeBrucella anthracis 0.001 0.01 0.007 positiveDiplococcus pneumoniae 0.005 11 10 positiveEscherichia coli 100 0.4 0.1 negativeKlebsiella pneumoniae 850 1.2 1 negativeMycobacterium tuberculosis 800 5 2 negativeProteus vulgaris 3 0.1 0.1 negativePseudomonas aeruginosa 850 2 0.4 negativeSalmonella (Eberthella) typhosa 1 0.4 0.008 negativeSalmonella schottmuelleri 10 0.8 0.09 negativeStaphylococcus albus 0.007 0.1 0.001 positiveStaphylococcus aureus 0.03 0.03 0.001 positiveStreptococcus fecalis 1 1 0.1 positiveStreptococcus hemolyticus 0.001 14 10 positiveStreptococcus viridans 0.005 10 40 positive

The entries of the table are the minimum inhibitory concentration (MIC) in ug/ml, a measure of the effectiveness of the antibiotic. The MIC represents the concentration of antibiotic required to prevent growth in vitro. The covariate “gram staining” describes the reaction of the bacteria to Gram staining. Gram-positive bacteria are those that are

stained dark blue or violet; Gram-negative bacteria do not react that way.

B. Smoothing problem – One might think that if life expectancy is great the murder rate cannot be. But although murder does not take a huge toll on a population perhaps it is an indicant of other life-threatening processes going on in society.

(a) Plot life expectancy as a function of murder rate, then (b) smooth life expectancy by adding the 53h smooth to the plot. What have you learned?(c) Make a separate plot of residuals from the smooth vs. murder rate. What has this taught you?(d) Add a straight-line fit to the plot. Does this help us to understand things better? Or does it hide things that the smooth has told us? Explain.

STATE NAMELIFE EXPECT. MURDER HSGRAD INCOME ILLITERACY

Alabama 69.1 15.1 41.3 3624 2.1Alaska 69.3 11.3 66.7 6315 1.5Arizona 70.6 7.8 58.1 4530 1.8Arkansas 70.7 10.1 39.9 3378 1.9California 71.7 10.3 62.6 5114 1.1Colorado 72.1 6.8 63.9 4884 0.7Connecticut 72.5 3.1 56.0 5348 1.1Delaware 70.1 6.2 54.6 4809 0.9Florida 70.7 10.7 52.6 4815 1.3Georgia 68.5 13.9 40.6 4091 2.0Hawaii 73.6 6.2 61.9 4963 1.9Idaho 71.9 5.3 59.5 4119 0.6Illinois 70.1 10.3 52.6 5107 0.9Indiana 70.9 7.1 52.9 4458 0.7Iowa 72.6 2.3 59.0 4628 0.5Kansas 72.6 4.5 59.9 4669 0.6Kentucky 70.1 10.6 38.5 3712 1.6Louisiana 68.8 13.2 42.2 3545 2.8Maine 70.4 2.7 54.7 3694 0.7Maryland 70.2 8.5 52.3 5299 0.9Massachusetts 71.8 3.3 58.5 4755 1.1Michigan 70.6 11.1 52.8 4751 0.9Minnesota 73.0 2.3 57.6 4675 0.6Mississippi 68.1 12.5 41.0 3098 2.4Missouri 70.7 9.3 48.8 4254 0.8Montana 70.6 5.0 59.2 4347 0.6Nebraska 72.6 2.9 59.3 4508 0.6

Nevada 69.0 11.5 65.2 5149 0.5NewHampshire 71.2 3.3 57.6 4281 0.7NewJersey 70.9 5.2 52.5 5237 1.1NewMexico 70.3 9.7 55.2 3601 2.2NewYork 70.6 10.9 52.7 4903 1.4NorthCarolina 69.2 11.1 38.5 3875 1.8NorthDakota 72.8 1.4 50.3 5087 0.8Ohio 70.8 7.4 53.2 4561 0.8Oklahoma 71.4 6.4 51.6 3983 1.1Oregon 72.1 4.2 60.0 4660 0.6Pennsylvania 70.4 6.1 50.2 4449 1.0RhodeIsland 71.9 2.4 46.4 4558 1.3SouthCarolina 68.0 11.6 37.8 3635 2.3SouthDakota 72.1 1.7 53.3 4167 0.5Tennessee 70.1 11.0 41.8 3821 1.7Texas 70.9 12.2 47.4 4188 2.2Utah 72.9 4.5 67.3 4022 0.6Vermont 71.6 5.5 57.1 3907 0.6Virginia 70.1 9.5 47.8 4701 1.4Washington 71.7 4.3 63.5 4864 0.6WestVirginia 69.5 6.7 41.6 3617 1.4Wisconsin 72.5 3.0 54.5 4468 0.7Wyoming 70.3 6.9 62.9 4566 0.6

4. A. Exact exponential growth – Fred and Alice were born the same year, and each began life with $500. Fred added $100 each year but kept his treasure under his mattress so he earned no interest. Alice added nothing, but earned interest at 7.5% annually. After 25 years, Fred and Alice are getting married. Who has more money? How much does each have? Alice’s cousin Charlie thinks that Fred is a paranoid loser and that Alice is cheap. He used a combined strategy and added $100 a year and obtained 7.5% interest. How much did he have after 25 years? All three continued with their strategies in the hopes of using the money to fund retirement. How much did each have at age 65?

a. Generate accumulations for each person for 65 yearsb. Plot both series.c. Answer the questions.d. Fit linear function to Frede. Based on this experiment which retirement savings strategy

works better, (a) add money regularly or (b) start early.

B. In Table 2 below are a number of state statistics. Some are correct and some are made up.

a. Through plots, correlations and regression lines discuss the relationship between the correct data and their imaginary counterparts.

b. Compare the four NAEP scores and see if the mean NAEP score adequately represents all states.

c. How would you characterize Gore and Bush states vis-à-vis their income and academic performance?

d. Has this characterization changed for the 2004 election?e. And what about obesity (Table 3)? Include in your

answer some discussion of fat blue states and thin red ones (i.e. states with large residuals).

Table 2. Correct state data on income and academic accomplishment 

Median NAEP Scores

State Income Math-4 Rdg - 4 Math-8 Rdg-8mean NAEP

'00 election IQ

FakeIncome

Massachusetts $50,587 242 228 287 273 257 Gore 111 24059New Hampshire $53,549 243 228 286 271 257 Bush 102 18834Vermont $41,929 242 226 286 271 256 Gore 102 20049Minnesota $54,931 242 223 291 268 256 Gore 113 26979Connecticut $53,325 241 228 284 267 255 Gore 99 18287North Dakota $36,717 238 222 287 270 254 Bush 111 26457South Dakota $38,755 237 222 285 270 254 Bush 100 18226Montana $33,900 236 223 286 270 254 Bush 100 18727Wyoming $40,499 241 222 284 267 253 Bush 102 20398Iowa $41,827 238 223 284 268 253 Gore 109 23534New Jersey $53,266 239 225 281 268 253 Gore 103 21451Virginia $49,974 239 223 282 268 253 Bush 99 18202Kansas $42,523 242 220 284 266 253 Bush 101 20253Maine $37,654 238 224 282 268 253 Gore 99 19508Colorado $49,617 235 224 283 268 252 Bush 104 21608Wisconsin $46,351 237 221 284 266 252 Gore 105 22974Ohio $43,332 238 222 282 267 252 Bush 107 20299North Carolina $38,432 242 221 281 262 252 Bush 106 21218Nebraska $43,566 236 221 282 266 251 Bush 101 21278Washington $44,252 238 221 281 264 251 Gore 92 15353Indiana $41,581 238 220 281 265 251 Bush 105 22934Missouri $43,955 235 222 279 267 251 Bush 92 16854New York $42,432 236 222 280 265 251 Gore 90 16558Delaware $50,878 236 224 277 265 250 Gore 90 16062Utah $48,537 235 219 281 264 250 Bush 89 17423Oregon $42,704 236 218 281 264 250 Gore 100 20629Idaho $38,613 235 218 280 264 249 Bush 96 19376Pennsylvania $43,577 236 219 279 264 249 Gore 99 20124Michigan $45,335 236 219 276 264 249 Gore 99 18624Illinois $45,906 233 216 277 266 248 Gore 93 17667Maryland $55,912 233 219 278 262 248 Gore 95 19084Kentucky $37,893 229 219 274 266 247 Bush 94 18043Texas $40,659 237 215 277 259 247 Bush 98 18835South Carolina $38,460 236 215 277 258 246 Bush 87 15325Florida $38,533 234 218 271 257 245 Bush 87 16067West Virginia $30,072 231 219 271 260 245 Bush 92 16534Alaska $55,412 233 212 279 256 245 Bush 92 17892Rhode Island $44,311 230 216 272 261 245 Gore 89 15989Oklahoma $35,500 229 214 272 262 244 Bush 98 19397

Georgia $43,316 230 214 270 258 243 Bush 93 15065Arkansas $32,423 229 214 266 258 242 Bush 98 21603Tennessee $36,329 228 212 268 258 241 Bush 90 16198Arizona $41,554 229 209 271 255 241 Bush 92 18130Nevada $46,289 228 207 268 252 239 Bush 92 15439Hawaii $49,775 227 208 266 251 238 Gore 94 17341California $48,113 227 206 267 251 238 Gore 94 17119Louisiana $33,312 226 205 266 253 238 Bush 99 20266Alabama $36,771 223 207 262 253 236 Bush 90 15712Mississippi $32,447 223 205 261 255 236 Bush 90 16220New Mexico $35,251 223 203 263 252 235 Gore 85 14088 NAEP data were gathered in February, 2003.

Table 3State % Obese Voted For State % Obese Voted For

Hawaii 17 Kerry Wisconsin 22 KerryColorado 17 Bush Nevada 22 BushConnecticut 18 Kerry Alaska 23 BushMassachusetts 18 Kerry Iowa 23 BushNew Hampshire 18 Kerry Kansas 23 BushUtah 18 Bush Missouri 23 BushCalifornia 19 Kerry Nebraska 23 BushMaryland 19 Kerry North Dakota 23 BushNew Jersey 19 Kerry Ohio 23 BushRhode Island 19 Kerry Oklahoma 23 BushVermont 19 Kerry Pennsylvania 24 KerryFlorida 19 Bush Arkansas 24 BushMontana 19 Bush Georgia 24 BushOregon 20 Kerry Indiana 24 Bush

Arizona 20 BushNorth Carolina 24 Bush

Idaho 20 Bush Virginia 24 BushNew Mexico 20 Bush Michigan 25 KerryWyoming 20 Bush Kentucky 25 BushMaine 21 Kerry Tennessee 25 BushNew York 21 Kerry Alabama 26 BushWashington 21 Kerry Louisiana 26 Bush

D.C 21 KerrySouth Carolina 26 Bush

South Dakota 21 Bush Texas 26 BushDelaware 22 Kerry Mississippi 27 BushIllinois 22 Kerry West Virginia 28 BushMinnesota 22 Kerry

Fat data fromNY Times Feb. 1, 2004Page 12Centers for Disease Control & Prevention

5. What is the pricing structure of convertibles? How would you answer someone who asked “how much does a convertible cost? Do the costs of convertibles fall into specific groups?” A transformation is most useful in the revelation of the underlying price structure. Include informative displays and a narrative explaining both what you did and what you found.

Car PriceAcura NSX-T $88,725 Aston Martin DB7 Volante $136,300 Audio Cabrio $35,100 Bentley Azure $329,400 BMW 318i $33,720 BMW 328i $41,960 BMW Z3 1.9 $29,995 BMW Z3 2.8 $36,470 Chevrolet Camaro $22,295 Chevrolet Camaro RS $23,695 Chevrolet Camaro Z28 $26,045 Chevrolet Cavalier LS $18,435 Chevrolet Corvette convertible $46,000 Chrysler Sebring JX $20,685 Chrysler Sebring JXi $25,295 Dodge Viper RT/10 $66,700 Ferrari F355 Spider $137,075 Ferrari F50 $487,000 Ford Mustang $21,280 Ford Mustang Cobra $28,660 Ford Mustang GT $24,510 Honda del Sol $15,475 Jaguar XK8 $70,480 Lamborghini Diablo Roadster VT $275,100 Mazda Miata M-Edition $24,935 Mazda MX-5 Miata $19,575 Mercedes-Benz SL320 $80,195 Mercedes-Benz SL500 $90,495 Mercedes-Benz SL600 $123,795 Mercedes-Benz SLK230 $40,295 Mitsubishi Eclipse Spyder GS $20,360 Mitsubishi Eclipse Spyder GS-T Turbo $26,200 Pontiac Firebird $23,609 Pontiac Firebird Formula $27,049 Pontiac Firebird Trans Am $28,969 Pontiac Sunfire SE $19,399 Porsche 911 Cabriolet $73,765 Porsche 911 Carrera 4 Cabriolet $79,115 Porsche Boxster $40,745 Saab 900 SE Talledega Turbo $42,520 Saab 900 SE Turbo $41,995 Saab 900 SE V6 $43,495

Saab 900S $36,195 Toyota Celica GT $24,858 Toyota Paseo $17,188 Volkswagon Cabrio $18,425 Volkswagon Cabrio Highline $22,175

Source: The New York Times8-Jun-97Section 11, page 1

B. In the table below are life insurance premiums. Find the underlying policy that Jackson National applied in setting rates for the four groups shown. HINT: plotting rates will help you uncover a sensible transformation, after which some sort of decomposition may be helpful. Accompany your result with a descriptive narrative.

Jackson National's 10 Year Level-term PolicyMonthly Life Insurance Premiums for $100,000

Male Female

AgeNonSmoke

r Smoker   NonSmoker Smoker30 12.34 22.34 10.85 17.7131 12.51 23.23 11.03 17.8932 12.69 24.21 11.29 18.0733 12.78 25.19 11.46 18.2534 13.04 26.26 11.55 18.4235 13.21 27.41 11.81 18.6036 13.74 29.01 12.16 19.4937 14.35 30.71 12.51 20.4738 14.96 32.57 12.95 21.5439 15.58 34.53 13.39 22.6140 16.28 36.67 13.91 23.8541 17.15 39.25 14.44 25.1042 17.94 42.10 15.05 26.4343 18.81 45.12 15.66 27.8644 19.78 48.51 16.28 29.3745 20.83 52.07 17.06 30.9746 22.14 55.18 17.85 32.6647 23.63 58.56 18.73 34.4448 25.20 62.21 19.60 36.4049 27.04 66.04 20.65 38.4550 28.79 70.13 21.70 40.6751 30.63 74.67 22.75 43.2552 32.64 79.57 23.89 46.0153 34.83 84.73 25.11 49.0454 37.01 90.34 26.43 52.2455 39.55 96.30 27.83 55.7156 42.53 103.06 29.14 58.6557 45.76 110.27 30.71 61.6858 49.35 118.01 32.29 64.9759 53.20 126.38 34.13 68.3560 57.31 135.37 35.88 72.0061 63.35 150.77 39.29 79.30

62 70.18 168.03 43.23 87.4063 77.61 187.35 47.51 96.3964 85.93 208.97 52.41 106.3665 95.38 233.18 57.75 117.4866 106.49 260.59 63.18 130.5667 119.26 291.30 69.30 145.2568 133.70 325.74 75.95 161.7169 149.89 364.37 83.30 180.0570 168.09 407.62 91.44 200.52

6. Fit a linear model to an average male’s growth and compare its predictions with the growth of Robert Wadlow. What characterizes Wadlow’s deviance (Slope? Intercept? Both?). Would a logistic function fit the data better? An advanced project might be to fit the sum of two logistics; try it only if you feel adventuresome.

Average Male Robt. WadlowAge HT(in) HT(in)

1 30.12 34.13 37.94 41.45 44.6 60.06 47.47 49.9

7.5 50.98 51.9 72.09 53.7 74.5

10 55.5 77.011 57.5 79.012 60.4 82.513 63.8 86.0

13.5 65.414 66.8 89.5

14.5 67.815 68.6 92.0

15.5 69.216 69.6 94.5

16.5 69.917 70.1 96.5

17.5 70.218 70.3 99.5

18.5 70.4

19 70.5 101.520 103.521 104.522 107.0

.

7. A. Decompose the table below using iterative median polish and display the final result in a compelling tabular format. Then display the result graphically. Accompany your result with a verbal description of what you have found.

           Infant Mortality-rates in the United State, all races, 1964-

1966(Entries are numbers of deaths per 1000 live births)

Education of fatherRegion <8 9 to 11 12 13-15 >16Northeast 25.3 25.3 18.2 18.3 16.3North Central 32.1 29.0 18.8 24.3 19.0South 38.8 31.0 19.3 15.7 16.8West 25.4 21.1 20.3 24.0 17.5

B. Reanalyze the data in (A) above using means. Compare the results of the two analyses.

C. Find a table of reasonable size (e.g. at least 5 x 10) in a scientific journal of your choice (e.g. Journal of the American Medical Association, Science, Nature, Psychological Bulletin, etc.) and:(i) Revise it according to the rules in Reference 20 or Ref. 14, chapter 10).(ii) Describe what you found that was not obvious initially.Be sure to include the initial table, the revision, and details about where the table came from and what the inferences that the original authors were making from the table.

8. A. In the relatively recent past there was a news article in the paper that reported that circumcision among men helped to prevent cervical cancer among women.

a. Describe what sorts of data were likely to have been used to derive this causal conclusion.

b. What would be the ideal data gathering experiment to allow such an inference?

c. How close is (a) to (b)? B. Schools sometimes advise parents that their child’s

academic future would be rosier if she/he repeated kindergarten.a. What sorts of prior evidence do you think the teacher was using

to justify such a recommendation?

b. What would be the ideal data gathering experiment to allow such an inference?

c. How close is (a) to (b)?

9. M&M (12.38 in 7th edition) Do poets die young? Parts a, b, c, 10. Cereals were analyzed by their protein content. It was also noted that different

kinds of cereal were placed on different shelves. The mean and standard deviation of protein content are shown in the table below by shelf position as is the results of an analysis of variance and box plots of the results.

Analysis of Variance

Sum of MeanSource Squares DF Square F-ratio P-valueShelf 12.4 2 6.2 5.8 0.004Error 78.7 74 1.1Total 91.1 76

Means and Std. Deviations

Shelf StandardLevel n Mean Deviation

1 20 2.65 1.462 21 1.90 0.993 36 2.86 0.72

a) What are the null and alternative hypotheses being tested in the ANOVA

b) What does the ANOVA results say about the null hypothesis? Be sure to report in terms of protein content and shelves.

c) Can we conclude that cereals on shelf 2 have a lower mean protein content than cereals on shelf 3? Can we conclude that cereals on shelf 2 have a lower mean protein content than cereals on shelf 1? What can we conclude?

d) To check for significant differences between the shelf means we can use a Bonferroni test, do so and show all of the pairwise comparisons. What does it say about the questions in part c?

11. M&M 12.38 in 7th edition– this time answer question (f) doing all pair-wise comparisons using the Bonferroni inequality with an overall = 0.05.

12. University of Pennsylvania Professor Ted Hershberg uses the results obtained by North Carolina researcher William Sanders in his plans to revamp American Public education. Specifically, he cites Sander’s finding that quality of teachers are the largest factor in students’ performance; that big improvements in student performance are caused by their teacher. Sanders makes this inference by looking at the gain (value-added) in test scores for each student over the year that student was in a specific teacher’s class and adjusts for all other factors by using them as covariates.

a. What issues would concern you about this inference?b. How would you design a study that would allow such inferences?c. How close do you think the data-gathering scheme from

Sanders’ observational study in Tennessee comes to the ideal case you have described in (b)?