Statistics A2

2.1 For each of the following studies, identify the type of graph (histogram, time series graph, or scatter diagram) that would be the most appropriate. (You can use more than one graph of each type, for example, two histograms.)

a. Are stock returns more volatile than bond returns?

b. Do interest rates affect home construction?

c. Is the rate of inflation higher or lower now than in the past?

d. Do cigarette sales depend on cigarette prices?

e. Is there more variation in the unemployment rate or the rate of inflation?

2.3 For each of the following studies, identify the type of graph (histogram, time series graph, or scatter diagram) that would be the most appropriate. (You can use more than one graph of each type, for example, two histograms.)

a. Do countries with lots of smokers have lots of lung-cancer deaths?

b. Does the time between eruptions of the Old Faithful geyser depend on the duration of the preceding eruption?

c. Is there more variation in annual rainfall in Los Angeles or in New York?

d. Have temperatures in Los Angeles gone up or down over the past 100 years?

e. Could the states that Mitt Romney won and lost in 2012 have been predicted from how well John McCain did in each state in 2008?

2.5 Use the data in Table 1.4 to make a histogram of the US dollar prices of a Big Mac in these 20 countries. Use these intervals for the prices: 1–2, 2–3, 3–4, 4–5, 5–8.

2.14 Do not collect any data, but use your general knowledge to draw a rough sketch of a histogram of the ages of the students at your school. Be sure to label the horizontal and vertical axes.

2.17 Use the data in Table 1.11 to make a time series graph of the real cost of mailing a letter.

2.19 Explain why you think the following pairs of data are positively related, negatively related, or essentially unrelated. If you think there is a causal relationship, which is the explanatory variable?

a. The height of a father and the height of his oldest son.

b. The age of a mother and the age of her oldest child.

c. The number of scalp hairs and the age of a man between the ages of 30 and 40.

d. A woman’s pre-pregnancy weight and the weight of her baby.

e. A woman’s age and her cost of a 1-year life insurance policy.

2.27 Plutonium has been produced in Hanford, Washington, since the 1940s, and some radioactive waste has leaked into the Columbia River. A 1965 study of cancer incidence in nearby communities [17] compared an exposure index and the cancer mortality rate per 100,000 residents for nine Oregon counties:

Which variable is the explanatory variable and which is the dependent variable? Make a scatter diagram and describe the relationship as either positive, negative, or nonexistent.

2.32 In 1974, Congress tried to reduce US fuel usage by imposing a nationwide 55 miles per hour speed limit. As time passed, motorists increasingly disregarded this speed limit; and in 1987, the speed limit on rural interstate highways was increased to 65 miles per hour. Plot the data on US motor vehicle deaths per 100 million miles driven, shown in Table 2.15, and see if anything unusual seems to have happened in 1974 and during the next several years.

2.34 What is misleading about Figure 2.34, which shows the distribution of family income? Redraw the figure, correcting these errors. (Be sure to say how you would define the middle class.)

2.35 What is wrong with the histogram in Figure 2.35?

2.36 What is wrong with the histogram in Figure 2.36?

2.37 What is wrong with the histogram in Figure 2.37?

2.38 What is wrong with the histogram in Figure 2.38?

2.39 What is wrong with the histogram in Figure 2.39 that was constructed from

annual rainfall data for the years 1901–2000? (Density is the rainfall for each year

divided by the total rainfall for all 100 years.)