9.4a. There are a couple of things you can do to emphasize the distinction. Probably the most important is to group the parents, teachers and students in 3 adjacent bars, then have a gap, and group the professors and employers in adjacent bars. Use only the percentages who answered "yes."
9.7There are many features that could be mentioned. Here are some. The picture is labeled well and the message is clear. The source is given as a textbook, so the original source is missing. The most obvious problem is that neither of the axes starts at zero, so the reader would have to be careful to notice that. No information is provided about how many golfers were included, so it is hard to know how accurate the percentages are in terms of representing all golfers.
9.10a. The pie chart should have four segments, with about 46% labeled as Type A, 8% as Type B, 4% as Type AB and 43% as Type O. (Notice that the total is 101% due to rounding; adjust the picture accordingly.)
b. Draw a bar graph with 16 bars. There are a number of ways to do the grouping of the bars. If you want to compare Caucasian Americans with African Americans you would picture them side by side for each of the eight blood types. If you wanted to compare Rh+ with Rh-, you would picture them side by side for each of the eight groups of blood type by race. There are other possibilities as well.
10.5The sample of size 10,000 would be more likely. To quote the textbook, "Even a minor relationship will achieve ‘statistical significance’ if the sample is very large" (p. 183).
10.9Correlation measures only how closely the points fall to a straight line. A perfect curved relationship where the best line through the points is flat would have a zero correlation. For example, draw x versus x2 for x = -3, −2, −1, 0, 1, 2, 3.
10.10a.Predicted GPA = 0.539 + (.00362)(500) = 2.349.
b.For each increase of 1 in verbal SAT score we would expect to see an increase of 0.00362 in GPA.
c.No. It would be the GPA for someone with an SAT score of 0, but that's not a possible score for the SAT.
10.14a.Success rate = 76.5 − (3.95)(6.5) = 50.825%.
b.For each additional foot of distance, success drops by about 3.95%.
11.4a.See Figure 11.1 below.
b.If X-rays were deleted, the correlation would decrease (to 0.13 in case you are interested), because outliers that fall in line with the rest of the data tend to increase correlation. If pesticides were deleted (but not X-rays) correlation would increase (to 0.68), because outliers that do not fit the pattern of the rest of the data tend to decrease correlation.
c.That would decrease the correlation because it would be an extreme outlier, not in line with the data. It also makes sense that it should decrease the correlation because it is an example of a case in which the students and experts are not in agreement at all, and thus weakens the relationship.
Figure 11.1 for Exercise 11.4a
11.8There would automatically be a relationship between the actual numbers, because large cities would have higher numbers for both than small cities. The more meaningful question is whether or not the per capita figures for beer sales and highway deaths are related.
11.12a.The most likely reason is that both change over time. A secondary reason may be that higher beer sales are contributing to more deaths from automobiles, but that would be indicated by higher rates for both, not by higher raw numbers.
b.The most likely reason is that there is a common cause, namely number of people at the resort that day. Obviously, temperature, snow conditions and day of the week all affect attendance, which in turn affects both accidents and waiting time.
c.Because the problem mentions that barbecued foods are known to contain cancer-causing substances, there is likely to be a direct causal link. Either direct cause alone, or contributing cause, would be acceptable answers.
d.There are a few possibilities here. There may just be a third variable causing both, namely personality type. More high-strung people would both see themselves as being under stress and have high blood pressure. Stress could also be a contributing, but not the sole, cause of high blood pressure. A weaker explanation is that high blood pressure causes stress, because people worry about having high blood pressure.
e.There are too many possible confounding factors to say that there is a direct cause. It could be that those who eat more fat also exercise less, for example. So, confounding variables make it difficult to determine a causal link.
f.Most likely this would be a coincidence. There would be unlikely to be enough cases at each school to conclude that it was anything else.
11.13Just like for the earthquake example in the text, the number of deaths is highly dependent on the density of houses in the area. Large fires are actually more likely to occur in sparse, wooded areas, where there are fewer people. Therefore, the relationship may actually be negative, giving the impression that the more acres burned, the fewer the number of deaths. Also, one or two outliers with relatively low acreage but high number of deaths could completely distort the results.
12.1No, it is not sufficient. We do not know how many of the men or women were Democrats versus Republicans.
12.6a.Observational study.
b.Reasons 3, 4 and 5 are all possibilities. Reason 3 says that firing someone or having a high-stakes deadline may be a contributor to the heart attack. Reason 4 says that there may be confounding variables; in this case, overall job responsibility and consequent stress are likely to be involved. Reason 5, that both having to fire someone (or having a deadline) and having a heart attack result from a common cause is possible; they could both indirectly result from having the type of personality that leads one to be driven to succeed, to take high risks, and so on.
c.i.A person who has to fire someone or is subjected to a high-stakes deadline has double the odds of having a heart attack in the following week than someone who has not had to do those things. (Notice that this is not the same thing as saying this person has twice the odds that that same person would have had if they hadn't fired someone or had the deadline.)
ii. Although someone who has to fire someone or who has a high-stakes deadline has twice the risk of having a heart attack during the next week as someone who has not done those things, the increased risk is quite small. For a healthy 50-year-old man or 60-year-old woman, the risk in any given hour without a trigger is only about 1 in a million.
iii. A person who has to fire someone or is subjected to a high-stakes deadline has twice the risk of having a heart attack in the following week than someone who has not had to do those things.
12.14a.Here is the combined table:
Admit / Deny / Total / Percent AdmittedMen / 450 / 550 / 1,000 / 450/1,000 = 45%
Women / 175 / 325 / 500 / 175/500 = 35%
Total / 625 / 875 / 1,500
A higher percentage of men than women were admitted, so it appears that the women could have been discriminated against.
b.Program A admitted 400/650 = 61.5% of the men, and 50/75 = 67% of the women. Program B admitted 50/350 = 14.3% of the men and 125/425 = 29.4% of the women. Therefore, it appears that both programs had a slight discrimination against men!
c.Simpson's Paradox occurs when combining groups reverses the direction of the relationship from what it was when the groups were separate. In this case, each program admitted a higher percentage of women, yet overall a lower percentage of women were admitted. What happened was that Program B was harder to get into, and was the one for which the majority of women applied. Of the applicants to Program A, which was relatively easy to get into, only about 10% were women. However, over half of the applicants to Program B, which was hard to get into, were women. These may have been something like Mathematics (Program A) and Psychology (Program B).
12.16a.The odds are 1,382 to 130, or about 10.6 to 1 for African Americans and 2,813 to 87 or about 32.3 to 1 for Caucasians.
b.Odds ratio is (2,813/87) (1,382/130) = 3.04.