Unit 4 Review
AP Statistics
Name
Period
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1. Which of the following scatterplots would indicate that Y is growing exponentially over time?
(a)
(b)
(c)
(d)
(e) none of these
2. A biologist plotted data from an experiment. He was interested in obtaining a least squares regression
line. However, the data did not appear to be linear, so a variety of transformations were applied. Based
on the following residual plots, which transformation was most effective in linearizing the data?
(a)
(b)
(c)
(d)
(e)
3. I measure a response variable Y at each of several times. A scatterplot of log Y versus time of
measurement looks approximately like a positively sloping straight line. We may conclude that
(a) the correlation between time of measurement and Y is negative, since logarithms of positive
fractions (such as correlations) are negative.
(b) the rate of growth of Y is positive but slowing down over time.
(c) an exponential curve would approximately describe the relationship between Y and time.
(d) a power function would approximately describe the relationship between Y and time.
(e) A mistake has been made. It would have been better to plot log Y versus the logarithm of time.
A review of voter registration records in a small town yielded the following table of the number of males and
females registered as Democrat, Republican, or some other affiliation.
Democrat
Republican
Other
Male
Female
300
500
200
600
300
100
4. The proportion of males that are registered as Democrats is
(a) 300.
(b) 0.33.
(c) 0.30.
(d) 0.15.
5. The proportion of all voters who are male and registered as Democrats is
(a) 300.
(b) 0.33.
(c) 0.30.
(d) 0.15.
(e) 0.375.
(e) 0.375.
Consider the two-way table of data at the right.
6. The percent of cars listed in the table with
4-cylinder engines that are made in Germany is
(a) 10.5%.
(b) 21%.
(c) 50%.
(d) 80%.
(e) 91%.
7. What percent of cars made in the U.S.A have engines
with more than 4-cylinders?
(a) 18,4%
(b) 31.8%
(c) 36.8%
(d) 39.5%
(e) 68.2%
8. The following two-way table categorizes superpower desired in a particular year by the gender of
college students who choose to participate.
Superpower
Flying
Invisibility
X-Ray Vision
Other
Male
13,959
3,148
3,222
1,457
Female
2,641
2,469
709
690
Which of the following statements is consistent with the table?
(a) There is absolutely no evidence of a relation between the gender of the college student and
superpower desired.
(b) More women participated in the survey than men.
(c) Men display a greater tendency to desire the ability to fly than do women.
(d) The correlation between superpower and gender is clearly positive.
(e) Females prefer invisibility over any other superpower.
Part 2: Free Response Answer completely, but be concise. Show your thought process clearly.
9. The table below presents Census Bureau data on the years of school completed by Americans of
different ages. Many people under 25 years of age have not completed their education, so they are left out
of the table. The entries in the table are the counts of persons in each age-by-education class. Although
both age and education in this table are categorical variables, both have a natural order from least to most.
The order of the rows and columns in the table reflects the order of the categories.
Years of school completed, by age, 2000 (thousands of persons)
Age group
Education
25 to 34
35 to 54
55+
Did not complete high school
4,474
9,155
14,224
Completed high school
11,546
26,481
20,060
1 to 3 years of college
10,700
22,618
11,127
4 or more years of college
11,066
23,183
10,596
Total
37,786
81,435
56,008
Total
27,853
58,087
44,445
44,845
175,230
(a) Calculate the marginal distribution of education level.
(b) Calculate the conditional distribution of age group, given “did not complete high school.”
(c) Make a bar graph to display the conditional distribution from (b). Be sure to label your graph.
(d) Describe what the graph in (c) tells you.
10. An experiment was conducted to determine the effect of practice time (in seconds) on the percent of
unfamiliar words recalled. Here is a Fathom scatterplot of the results with a least-squares regression line
superimposed.
(a) Sketch a residual plot below.
(b) Does a linear model fit the data well? Justify your
answer.
We used Fathom to transform the original data in hopes of achieving linearity. The screen shots below
show the results of two different transformations.
(c) Which model would fit the original data better, an exponential model or a power model? Justify your
answer.
(d) Use the model you chose in (c) to predict word recall for 25 seconds of practice. Show your method.
Answer Key
1) D 2) D
3) C
4) C
5) D
6) A
7) E
8) C