II.1. Poverty in the states. Table II.1 gives the percentages of people living below the poverty line in the 26 states east of the Mississippi River. Make a stemplot of these data. Is the distribution roughly symmetric, skewed to the right, or skewed to the left? Which states (if any) are outliers? (Hint: See page 253.)

II.2. Quarterbacks. Table II.2 gives the total passing yards for National Football League starting quarterbacks during the 2014 season. (These are the quarterbacks with the most passing yards on each team.) Make a histogram of these data. Does the distribution have a clear shape: roughly symmetric, clearly skewed to the left, clearly skewed to the right, or none of these? Which quarterbacks (if any) are outliers?

II.3. Poverty in the states. Give the five-number summary for the data on poverty from Table II.1. (Hint: See page 272.)

II.4. Quarterbacks. Give the five-number summary for the data on passing yards for NFL quarterbacks from Table II.2.

II.5. Poverty in the states. Find the mean percentage of state residents living in poverty from the data in Table II.1. If we removed Mississippi from the data, would the mean increase or decrease? Why? Find the mean for the 25 remaining states to verify your answer. (Hint: See page 277.)

II.6. Big heads? The army reports that the distribution of head circumference among male soldiers is approximately Normal with mean 22.8 inches and standard deviation 1.1 inches. Use the 68–95–99.7 rule to answer these questions.

II.7. SAT scores. The scale for SAT exam scores is set so that the distribution of scores is approximately Normal with mean 500 and standard deviation 100. Answer these questions without using a table.

II.8. Explaining correlation. You have data on the yearly wine consumption (liters of alcohol from drinking wine per person) and yearly deaths from cirrhosis of the liver for several developed countries. Say as specifically as you can what the correlation r between yearly wine consumption and yearly deaths from cirrhosis of the liver measures.

II.9. Data on snakes. For a biology project, you measure the length (inches) and weight (ounces) of 12 snakes of the same variety. What units of measurement do each of the following have?

II.10. More data on snakes. For a biology project, you measure the length (inches) and weight (ounces) of 12 snakes of the same variety.

Figure II.3 plots the average brain weight in grams versus average body weight in kilograms for many species of mammals. There are many small mammals whose points at the lower left overlap. Exercises II.11 through II.16 are based on this scatterplot.

II.11. Dolphins and hippos. The points for the dolphin and hippopotamus are labeled in Figure II.3. Read from the graph the approximate body weight and brain weight for these two species. (Hint: See page 318.)

II.12. Dolphins and hippos. One reaction to this scatterplot is “Dolphins are smart; hippos are dumb.’’ What feature of the plot lies behind this reaction?

II.13. Outliers. African elephants are much larger than any other mammal in the data set but lie roughly in the overall straight-line pattern. Dolphins, humans, and hippos lie outside the overall pattern. The correlation between body weight and brain weight for the entire data set is r = 0.86.

II.14. Brain and body. The correlation between body weight and brain weight is r = 0.86. How well does body weight explain brain weight for mammals? Compute r² to answer this question, and briefly explain what r² tells us.

II.15. Prediction. The line on the scatterplot in Figure II.3 is the least-squares regression line for predicting brain weight from body weight. Suppose that a new mammal species with body weight 600 kilograms is discovered hidden in the rain forest. Predict the brain weight for this species. (Hint: See page 340.)

II.16. Slope. The line on the scatter-plot in Figure II.3 is the least-squares regression line for predicting brain weight from body weight. The slope of this line is one of the numbers below. Which number is the slope? Why?

From Rex Boggs in Australia comes an unusual data set: before showering in the morning, he weighed the bar of soap in his shower stall. The weight goes down as the soap is used. The data appear in Table II.3 (weights in grams). Notice that Mr. Boggs forgot to weigh the soap on some days. Exercises II.17, II.18, and II.19 are based on the soap data set.

II.17. Scatterplot. Plot the weight of the bar of soap against day. Is the overall pattern roughly straight-line? Based on your scatterplot, is the correlation between day and weight close to 1, positive but not close to 1, close to 0, negative but not close to −1, or close to −1? Explain your answer. (Hint: See page 325.)

II.18. Regression. The equation for the least-squares regression line for the data in Table II.3 is

weight = 133.2 − 6.31 × day

II.19. Prediction? Use the regression equation in the previous exercise to predict the weight of the soap after 30 days. Why is it clear that your answer makes no sense? What’s wrong with using the regression line to predict weight after 30 days? (Hint: See page 345.)

II.20. Keeping up with the Joneses. The Jones family had a household income of $30,000 in 1980, when the average CPI (1982–84 = 100) was 82.4. The average CPI for 2014 was 236.7. How much must the Joneses earn in 2014 to have the same buying power they had in 1980?

II.21. Affording a Mercedes. A Mercedes-Benz 190 cost $24,000 in 1981, when the average CPI (1982–84 = 100) was 90.9. The average CPI for 2014 was 236.7. How many 2014 dollars must you earn to have the same buying power as $24,000 had in 1981? (Hint: See page 372.)

II.22. Affording a Steinway. A Steinway concert grand piano cost $13,500 in 1976. A similar Steinway cost $163,600 in August 2015. Has the cost of the piano gone up or down in real terms? Using Table 16.1 and the fact that the August 2015 CPI was 238.7, give a calculation to justify your answer.

II.23. The price of gold. Some people recommend that investors buy gold “to protect against inflation.’’ Here are the prices of an ounce of gold at the end of the year for the years between 1985 and 2013. Using Table 16.1, make a graph that shows how the price of gold changed in real terms over this period. Would an investment in gold have protected against inflation by holding its value in real terms?

(Hint: See page 372.)

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II.24. Never on Sunday? The Canadian province of Ontario carries out statistical studies to monitor how Canada’s national health care system is working in the province. The bar graphs in Figure II.4 come from a study of admissions and discharges from community hospitals in Ontario. They show the number of heart attack patients admitted and discharged on each day of the week during a two-year period.

II.25. Drive time. Professor Moore, who lives a few miles outside a college town, records the time he takes to drive to the college each morning. Here are the times (in minutes) for 42 consecutive weekdays, with the dates in order along the rows:

II.26. Drive time outliers. In the previous exercise, there are three outliers in Professor Moore’s drive times to work. All three can be explained. The low time is the day after Thanksgiving (no traffic on campus). The two high times reflect delays due to an accident and icy roads. Remove these three observations. To summarize normal drive times, use a calculator to find the mean and standard deviation s of the remaining 39 times.

II.27. House prices. An April 15, 2014, article in the Los Angeles Times reported that the median housing price in Southern California was about $400,000. Would the mean housing price be higher, about the same, or lower? Why? (Hint: See page 281.)

II.28. The 2012 election. Barack Obama was elected president in 2012 with 51.1% of the popular vote. His Republican opponent, Mitt Romney, received 47.2% of the vote, with minor candidates taking the remaining votes. Table II.4 gives the percentage of the popular vote won by President Obama in each state. Describe these data with a graph, a numerical summary, and a brief verbal description.

II.29. Statistics for investing. Joe’s retirement plan invests in stocks through an “index fund’’ that follows the behavior of the stock market as a whole, as measured by the Standard & Poor’s 500 index. Joe wants to buy a mutual fund that does not track the index closely. He reads that monthly returns from Fidelity Technology Fund have correlation r = 0.77 with the S&P 500 index and that Fidelity Real Estate Fund has correlation r = 0.37 with the index.

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