Text material for Homework posted first on Day 4. [ ] are Sievers’s comments, additions

p. 64-5, 2.46 Activity/obesity: People gain weight when they take in more energy from food than they expend. Table 2.4 compares volunteer subjects who were lean with others who were mildly obese. None of the subjects followed an exercise program. The subjects wore sensors that recorded every move for 10 days. The table shows the average minutes per day spent in activity (standing and walking) and in lying down. 16 Compare the distributions of time spent actively for lean and obese subjects and also the distributions of time spent lying down. How does the behavior of lean and mildly obese people differ?

[Use the 4-step process, see Day4, bottom, p. 55-7&/or inside front cover. Note that "state", the first step, is usually "done"= the textbook statement of the problem.

Use back-to-back stemplots to plot the data. That, medians, and ranges (highest-lowest) should be enough here, plus discussion and description. (With only ten observations each in front of you in stemplots, I think more computation is overkill. )]

p. 60, 2.28 Pulling wood apart [again]. Example 1.9 ( page 20) gives the breaking strengths of 20 pieces of Douglas fir. See Link for Mean/Median Questions, for data.

( a) Give the five- number summary of the distribution of breaking strengths. ( The stemplot, Figure 1.11, helps because it arranges the data in order, but you should use the unrounded values in numerical work.)

( b) The stemplot shows that the distribution is skewed to the left. Does the five-number summary show the skew? Remember that only a graph gives a clear picture of the shape of a distribution.

[Go ahead and use the stemplot figures to find the quartiles. Also make a boxplot.]

p. 60, 2.30 How much fruit do adolescent girls eat? Figure 1.14 ( page 30) is a histogram of the number of servings of fruit per day claimed by 74 seventeen- year- old girls. With a little care, you can find the median and the quartiles from the histogram. What are these numbers? How did you find them? [See Link for Day 2 questions, p. 2, for histogram.]

p. 61, 2.35 Guinea pig survival times. Here are the survival times in days of 72 guinea pigs after they were injected with infectious bacteria in a medical experiment. Survival times, whether of machines under stress or cancer patients after treatment, usually have distributions that are skewed to the right.

43 45 53 56 56 57 58 66 67 73 74 79

80 80 81 81 81 82 83 83 84 88 89 91

91 92 92 97 99 99 100 100 101 102 102 102

103 104 107 108 109 113 114 118 121 123 126 128

137 138 139 144 145 147 156 162 174 178 179 184

191 198 211 214 243 249 329 380 403 511 522 598

( a) Graph the distribution and describe its main features. Does it show the expected right skew?

( b) Which numerical summary would you choose for these data? Calculate your chosen summary. How does it reflect the skewness of the distribution?

[For a) use the One Variable Statistical Calculator Applet at http://bcs.whfreeman.com/bps5e or on your text's CD.Observe the skewness, sketch on your paper. For b), find the 5-number summary (easy since they're in order in the book), check your answers with the Applet results. Draw the boxplot and compare with the histogram on your screen. (marking or not marking outliers, I don't care.)]

p. 60, 2.27 University endowments. The National Association of College and University Business Officers collects data on college endowments. In 2007, 785 colleges and universities reported the value of their endowments. When the endowment values are arranged in order, what are the positions of the median and the quartiles in this ordered list?

[They mean, what do you have to count in to, in the list, to locate the mean and quartiles?]

p. 60, 2.29 Comparing tropical flowers. &

p. 61, 2.36 days of births, Canada (Toronto, actually)

On next pages (for page-space reasons)

p. 57 2.13 Logging in the rain forest. “ Conservationists have despaired over destruction of tropical rain forest by logging, clearing, and burning.” These words begin a report on a statistical study of the effects of logging in Borneo. Charles Cannon of Duke Uni versity and his coworkers compared forest plots that had never been logged ( Group 1) with similar plots nearby that had been logged 1 year earlier ( Group 2) and 8 years earlier ( Group 3). All plots were 0.1 hectare in area. Here are the counts of trees for plots in each group:

Group 1: 27 22 29 21 19 33 16 20 24 27 28 19

Group 2: 12 12 15 9 20 18 17 14 14 2 17 19

Group 3: 18 4 22 15 18 19 22 12 12

To what extent has logging affected the count of trees? Follow the four- step process in reporting your work.
[(Big picture--how fast does a forest recover from logging?) Use the 4-step process, see Day4, bottom, p. 55-7&/or inside front cover. The data are probably suitable for mean& standard deviation, but we don't have the SPSS power to do them easily yet, so use your hand methods--stemplots, quartiles, boxplots... This is one where working together with others can have real benefits, since it's pretty open-ended.]


p. 60, 2.29 Comparing tropical flowers. An alternative presentation of the flower length data in Table 2.1 reports the five- number summary and uses boxplots to display the distributions. Do this. Do the boxplots fail to reveal any important information visible in the stemplots in Figure 2.5?

[Find the 5-number summary for Yellows. You may use the stemplot data p. 57. If you want more practice, do the other 2 by hand also, but you may just use the numbers from the answers in the back of the book. Use them to make 3 side by side boxplots, and finish the problem as written.]


p. 61, 2.36 days of births, Canada (Toronto, actually) Never on Sunday: also in Canada? Exercise 1.5 ( page 11) gives the number of births in the United States on each day of the week during an entire year. The boxplots in Figure 2.6 are based on more detailed data from Toronto, Canada: the number of births on each of the 365 days in a year, grouped by day of the week. Based on these plots, give a more detailed description of how births depend on the day of the week.

[The book's question is very open-ended. Answer instead the questions just below the HW box, Day 4]

FIGURE 2.6 Boxplots of the distributions of numbers of births in Toronto, Canada, on each day of the week during a year, for Exercise 2.36.

Day / Births
Sun
Mon
Tues
Wed
Thur
Fri
Sat / 7,374
11,704
13,169
13,038
13,013
12,664
8,459

Table from 1.5 p. 11 Births

The average numbers of babies born on each day of the week in 2005 [in the U.S]