Midterm Exam Prep Solutions
Midterm Exam Prep Solutions
1.10. Exact descriptions of the populations may vary. (a) Teenagers (or “tenth-graders,” but from the description of the situation, the researcher would like information about all teens). (b) The most recent set of exams (or perhaps, all exams for the course). (c) All adults, or everyone (the radio host’s question does not necessarily exclude children from consideration).
1.16. The population is textbooks. The sample is all the books on the randomly selected rack at the local bookstore. The variables are number of pages and price.
2.9. Call-in polls (especially those that cost to call in), and voluntary response polls in general, tend to attract responses from those who have strong opinions on the subject, and therefore are often not representative of the population as a whole. A random sample of size 1,000 will ideally be representative of the population as a whole. While the 300,000 callers might be an impressive number, the voluntary response of these callers is not trustworthy.
3.20. The sample size for men is smaller than the sample size for women, so the results for men have more variability.
5.7. There may be some lurking difference between the students at the two universities. This would be confounded with the effect of the pleasant scent.
6.15. For each person, flip a coin to decide which hand they should use first (heads: right hand first; tails: left hand first). Record the difference in hand strength for each person.
8.8. This measures learned facts rather than general problem-solving ability.
8.20. It would almost certainly lead to underreporting, because victims of sexual assaults would likely be reluctant to discuss the incident in front of friends or relatives.
10.6. This graph is misleading because the cones used to represent each interest rate are scaled both horizontally and vertically—they suffer from the “pictogram defect.”
11.14. The distribution of the percentages of the population who are of Asian origin in each state east of the Mississippi River is skewed to the right. There appear to be two high outliers: New York (6.9%) and New Jersey (7.5%). Ignoring these outliers, the distribution is still skewed right, with a center around 2.0% and a range from 0.6% to 4.9%. Note: Your stemplot should contain a vertical line separating the stem from the leaf
0 68999
1 013358
2 00233789
3 3
4 2889
5
6 9
7 5
12.6. (a) The mean is greater than the median, because income distributions tend to be right skewed.
(b) Some respondents may have exaggerated their incomes (to impress either the
pollster or someone in the room with them as they answered the question).
13.15. Students may at first make mistakes like drawing a half-circle instead of the correct “bellshaped” curve, or being careless about locating the standard deviation.
14.25. (a) Substantial positive correlation. (b) Substantial negative correlation. (c) Substantial positive correlation. (d) Small correlation.
15.18. (a) The range of values on the horizontal axis may vary. Following the
instructions given in the text, this plot can be drawn by taking x = 0 years and y = $1,000, and x = 10 years and y = $2,000.
(b) When x = 20, y = $3,000. (c) y = 1,000 + 300x (The slope is his rate of savings, in dollars per year.)
15.26. A reasonable explanation is that the cause-and-effect relationship goes in the other direction: doing well makes students feel good about themselves, rather than vice versa.