Learning Problems Ch. 1
1.1 Television-viewing habits. You are preparing to study the television-viewing habits
of college students. Describe two categorical variables and two quantitative variables
that you might measure for each student. Give the units of measurement for the
quantitative variables. Also, what will the individuals in your data set be?
1.7 Automobile fuel economy. Table 1.2 (page 12) gives data on the fuel economy of
2006 model midsize cars. Based on a histogram of these data:
(a) Describe the main features (shape, center, spread, outliers) of the distribution of
highway mileage.
(b) The government imposes a “gas guzzler” tax on cars with low gas mileage.
Which of these cars do you think are subject to the gas guzzler tax.
1.39 Bank workers. Find the mean earnings of the remaining three groups in
Table 1.10. Does comparing the four means suggest that National Bank pays male
hourly workers more than females, or white workers more than blacks? (Of course,
detailed investigation of such things as job type and seniority is needed before we claim
discrimination.
1.41 Bank workers. Find the median earnings of the remaining three groups of workers
in Table 1.10. Do your preliminary conclusions from comparing the medians differ from
the results of comparing the mean earnings in Exercise 1.39? (Because the median is
not distorted by outliers, we might prefer to base an initial look at possible inequity on
the median rather than the mean.
1.80 Figure 1.19 displays the density curve of a uniform distribution. The curve takes
the constant value 1 over the interval from 0 to 1 and is 0 outside that range of values.
This means that data described by this distribution take values that are uniformly spread
between 0 and 1. Use areas under this density curve to answer the following questions.
(a) Why is the total area under this curve equal to 1?
(b) What percent of the observations lie above 0.8?
(c) What percent of the observations lie below 0.6?
(d) What percent of the observations lie between 0.25 and 0.75?
(e) What is the mean μ of this distribution?
FIGURE 1.19 The density curve of a uniform distribution, for Exercise 1.80.
1.82 Heights of young men. Product designers often must consider physical
characteristics of their target population. For example, the distribution of heights of men
aged 20 to 29 years is approximately Normal with mean 69 inches and standard
deviation 2.5 inches. Draw a Normal curve on which this mean and standard deviation
are correctly located. (Hint: Draw the curve first, locate the points where the curvature
changes, then mark the horizontal axis.)