AP Statistics
Chapter 4 Review
Name:_____________________________
***YOU WILL NEED TO USE YOUR OWN PAPER***
1. In physics class, the intensity of a 100-watt light bulb was measured by a sensing device at various distances from the light source,
and the following data were collected. Not that a candela (cd) is an international unit of luminous intensity.
Distance
(meters)
1.0
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Intensity
(candelas)
0.2965
0.2522
0.2055
0.1746
0.1534
0.1352
0.1145
0.1024
0.0923
0.0832
0.0734
(a) Plot the data. Based on the pattern of points, propose a model form for the data. Then use a transformation followed by linear
regression and then an inverse transformation to construct a model.
(b) Report the equation, and plot the original data with the model on the same axes.
(c) Is this model a good fit for the data? Why or why not?
(d) Find the predicted intensity of the light bulb at a distance of 1.58 meters.
2. Federal expenditures on social insurance increased rapidly after 1960. Here are the amounts spent, in millions of dollars:
Year:
Spending:
1960
14,307
1965
21,807
1970
45,246
1975
99,715
1980
191,162
1985
310,175
1990
422,257
(a) Plot social insurance expenditures against time. Does the pattern appear closer to linear growth or to exponential growth?
(b) Take the logarithm of the amounts spent. Plot these logarithms against time. Do you think that the exponential growth model fits
well?
(c) Find the LSRL for the transformed data. Find the correlation for the transformed data. Draw this line on your graph from (b).
(d) Using your LSRL, predict the expenditures for 1988.
For questions 3 through 5, state whether the relationship between the two variables involves causation, common response, or
confounding. Then identify possible lurking variable(s). Draw a diagram of the relationship in which each circle represents a
variable. By each circle, write a brief describtion of the variable.
3. There is a negative correlation between the number of flu cases reported each week throughout the year and the amount of ice
cream sold in that particular week. It’s unlike that ice cream prevents flu. What is a more plausible explanation for this observed
correlation?
4. A study finds that high school students who take the SAT, enroll in an SAT coaching course, and then take the SAT a second time
raise their SAT mathematics scores froom a mean of 521 to a mean of 561. What factors other than “taking the course causes higher
scores” might explain this improvement?
5. People who use artificial sweeteners in place of sugar tend to be havier than people who use sugar. Does this mean that artificial
sweeteners cause weight gain? Give a more plausible explanation for this association.
6. The number of people living on American farms has declinded steadily during this century. Here are data on the farm population
(millions of persons) from 1935 to 1980.
Year:
Population:
1935
32.1
1940
30.5
1945
24.4
1950
23.0
1955
19.1
1960
15.6
1965
12.4
1970
9.7
1975
8.9
1980
7.2
(a) Make a scatterplot of these data and find the LSRL of farm population on year.
(b) According to the regression line, how much did the farm population decline each year on average during this period (slope)?
What percent of the observed variation in farm population is acounted for by linear change over time (r2)?
(c) Use the regression equation to predict the number of people living on farms in 1990. Is this result reasonable? Why?
7. Here are data from eight high schools on smoking among students and among their parents.
Student does not smoke
Student smokes
Neither parent
smokes
1168
188
One parent
smokes
1823
416
Both parents
smoke
1380
400
(a) How many students do these data describe?
(b) What percent of these students smoke?
(c) Give the marginal distribution of parents’ smoking behavior, both in counts and in percents.
(d) Find the conditional distribution of student smokers.
8. Upper Wabash Tech has two professional schools, business and law. Here are two-way tables of applicants to both schools,
categorized by gender and admission decision.
Male
Female
Business
Admit
480
180
Deny
120
20
Male
Female
Law
Admit
10
100
Deny
90
200
(a) Make a two-way table of gender by admission decision for the two professional schools together by summing entries in this table.
(b) From the two-way table, calculate the percent of male applicants who are admitted and the percent of female applicants who are
admitted. Wabash admits a higher percent of male applicants.
(c) Now compute separately the percents of male and femal eapplicants admitted by the business school and by the law school. Each
school admits a higher percent of female applicants.
(d) This is Simpson’s paradox: both schools admit a higher percent of the women who apply, but overal Wabash admits a lower
percent of female applicants than of male applicants. Explain carefully, as if speaking to a skeptical reporter, how it can happen that
Wabash appears to favor males when each school individually favors females.