32. Systematic sampling.
34. Simple random sampling.
52. The proportion of people showing improvement in the treatment group was the same as the proportion of people showing improvement in the control group: there is no evidence that the treatment is effective.
60. (a) The goal of the study was to determine the
percentage of adult Americans who keep money in a regular
savings account. The population is all adult Americans;
the population parameter is percentage of all adult Americans
who keep money in a regular savings account.
(b) The sample consists of the 2000 adult Americans
surveyed; the sample statistic is the percentage of
those people who kept money in a savings account.
(c) The confidence interval is 64% plus or minus 2%,
namely, 62% to 66%.
Section 5B:
16. If the study confined itself to those who were randomly audited (a certain number of people are randomly audited each year), then there would be no reason to doubt the results of this study, based on the information given. If done properly, the audits should indeed discover whether an individual taxpayer understated his/her income, so with a large enough survey of random audits, it should be possible to make a good estimate of the rate at which this cheating occurs. However, if the study includes all the people who were audited, many of whom were selected for audit specifically because their tax returns sent up "red flags" and seemed suspicious, and hence were not chosen at random, then the study might overstate the tendency of taxpayers to understate their income.
18. There is no reason to doubt the results of this study based on the information given. Eating and activity levels are major factors in obesity, and the study appears to be monitoring both carefully. It's still possible there are other confounding variables (what sort of person consents to participate in such a study?), but there are no obvious candidates for a "third factor" that might invalidate the study.
Section 5C:
8. This makes sense. Relative frequency must be between 0 and 1, and this number is. It simply tells us that 30% of the class got B grades.
10. This makes sense. The point of a bar graph is to show frequencies for the various categories, so if yours are different from the correct answer, then either you are wrong or the answer key is wrong.
12. This makes sense. Pie charts show relative frequency and thus must always show a total of 100% (or maybe a few percentage points more or less, if rounding has occurred). If the relative frequencies are adding up to something that's 24 percentage points more or less than 100%, something must have gone wrong in their calculation.
16.
| Rating | Freq. | Rel. freq. | Cum. freq. |
| 5-star | 5 | 0.09 | 0.09 |
| 4-star | 10 | 0.18 | 0.27 |
| 3-star | 20 | 0.37 | 0.64 |
| 2-star | 15 | 0.27 | 0.91 |
| 1-star | 5 | 0.09 | 1.00 |
| Total | 55 | 1.00 |
26.
| Bin | Freq. | Rel. freq. | Cum. freq. |
| 90-99 | 4 | 0.16 | 0.16 |
| 80-89 | 9 | 0.36 | 0.52 |
| 70-79 | 5 | 0.20 | 0.72 |
| 60-69 | 4 | 0.16 | 0.88 |
| 50-59 | 2 | 0.08 | 0.96 |
| 0-49 | 1 | 0.04 | 1.00 |
| Total | 25 | 1.00 |
28. See the ASCII file I created (view it in fixed-width mode).
30. The pie-chart should have a 180-degree wedge labelled "4-year college 50%" (e.g., from 9 to 3 on the clockface), a 120-degree wedge labelled "2-year college 33%" (e.g., from 3 to 7 on the clockface), and a 60-degree wedge labelled "no college 17%" (e.g., from 7 to 9 on the clockface).
46. (a) In 1982, there were about 25,000 deaths.
In 2000, there were about 17,000 deaths. The overall trend
was a decrease in fatalities due to alcohol-related crashes.
(b) Using 25,000 as the reference value, the percent
change was (17,000-25,000)/25,000 = - 0.32 or a 32%
decrease in fatalities.
(c) In 1982, 25,000/43,945 = 0.569 or about 57% of
fatalities involved alcohol. In 2000, 17,000/41,821
= 0.406 or about 41% of fatalities involved alcohol.
(d) (not assigned) Note that the decrease in fatalities did
not decline as much in either absolute or relative terms as
fatalities involving alcohol. So, on the one hand, not as
many people are dying in crashes involving alcohol. On the
other hand, everything else being the same, there should
also have been a greater decrease in overall number of
fatalities. Some other factor in fatalities has increased
or there are perhaps new factors. More study is indicated.
Section 5D:
16. (a) In 1930, about 75,000 men and 50,000 earned
degrees; in 2000, about 500,000 men and 600,000 women did.
(b) In 1980, slightly more men than women earned degrees;
in 2000, more women than men earned degrees.
(c) The total number of degrees awarded increased most
during the 1960s.
(d) In 1950, about 450,000 degrees were awarded; in 2000,
about 1.15 million degrees were awarded.
22. (a) In 1860 about 35% of the population was in the
5- to 19-year-old category. In 1990, about 15% of the population
was in this category.
(b) In 1860 about 35% of the population was in the 20- to
44-year-old category. In 1990, about 40% of the population
was in this category.
(c) (not assigned) The percentage of under-5-year-olds
increased because of soldiers returning from overseas
and starting families at about the same time, and
post-war economic prosperity in the U.S. that made it
easier for young couples to afford to have children;
this demographic spike is called the "baby boom".
30. (a) Read this information directly from the
percentage change graph. The percent increase of public
college costs was greatest in 1991 at 12%. (Note that
the graph contains the explanatory words "Percentage
change from previous academic year", which explains
the meaning of the vertical axis.)
(b) Read this information directly from the same graph.
The same year, private college costs rose about 7%.
(c) Looking at the graph of actual costs, we see that
public college cost rose by less than $500, but private
college cost rose by nearly $1000. (You have to read
the change from the 90-91 school year to the 91-92
school year.) That is, when we move from 90-91 to
91-92, the blue rectangle gains more height than
the red rectangle. (Note that the fact that the
blue rectangles are bigger than the red rectangles
is not germane to the answer; all that this tells
us is that private colleges cost most than public
colleges, whereas what we're interested in is how
much change occurred from one year to the next.)
A different way to solve part (c) is as follows:
In 90-91, public college costs were about $2,000
(according to the top half of Figure 5.25), and
from 90-91 to 91-92 they rose by 12% (according
to the bottom half of Figure 5.25), so the relative
increase of 12% is an absolute increase of
12% times $2,000, or about $240. Meanwhile,
private college costs were about $10,000 in 90-91,
and in the following year they rose by about 7%,
so the absolute increase was 7% of $10,000, or
about $700. Since $700 is more than $240, we
see that the absolute (dollar-amount) increase
in private college tuition was higher than the
absolute increase in public college tuition.