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AP Statistics
Name_______________________________________________
Free response Practice: Chapters 1-4
Mr. Coppock/Mr. Dooley
1) The Better Business Council of a large city has concluded that students in the city’s schools are not
learning enough about economics to function in the modern world. These findings were based on test
results from a random sample of 20 twelfth-grade students who completed a 46 question multiple choice
test on basic economic concepts. The data set below shows the number of questions that each of the 20
students in the sample answered correctly.
12
16
18
17
18
33
41
44
38
35
19
36
19
13
43
8
16
14
10
9
(a) Display these data in a stemplot.
(b) Use your stemplot from part (a) to describe the main features of this score distribution.
(c) Why would it be misleading to report only a measure of center for this score distribution?
2) We all “know” that the body temperature of a healthy person is 98.6 °F. In reality, the actual body
temperature of individuals varies. Here is a back-to-back stemplot of the body temperatures of 130
healthy individuals (65 males and 65 females).
(a) Here are boxplots, produced by Minitab, for these
distributions. Label both boxplots with the 5-number
summary values.
Males
Females
96
97
98
99
100
101
(b) Determine whether the 3 points graphed by the +
symbol are indeed outliers by our defined criteria.
Males
Females
3
96
96
4
7
96
7
9
96
8
1110
97
32
97
22
544444
97
4
7666
97
677
998888
97
8888999
11000000
98
000001
332222
98
222222333
554444
98
444445
77666666
98
6666777777
9888
98
8888889
1000
99
0011
32
99
223
54
99
4
99
99
9
100
0
100
100
100
100
8
(c) Write a few sentences comparing the body temperatures of adult males and females.
3) A simple random sample of 9 students was selected from a large university. Each of these students
reported the number of hours he or she had allocated to studying and the number of hours allocated to
work each week. A least squares linear regression was performed and part of the resulting computer
output is shown below. (Note: exercise 3.35, on page 212 in your textbook shows you how to come up
with the regression equation from computer output. Or you can look at page 900 in your textbook for a
similar explanation.)
The scatterplot below displays the data that were collected from the 9 students.
(a) After point P, labeled on the graph, was removed from the data, a second linear regression was
performed and the computer output is shown below.
Does point P exercises a large influence on the regression line? Explain.
(b) The researcher who conducted the study discovered that the number of hours spent studying reported
by the students represented by P was recorded incorrectly. The correct data point for this student is
represented by the letter Q in the scatterplot below.
Explain how the least squares regression line for the corrected data (in this part) would differ from the
least squares regression line for the original data.
4.) The best male long jumpers for State College since 1973 have averaged a jump of 263.0 inches with a
standard deviation of 14.0 inches. The best female long jumpers have averaged 201.2 inches with a
standard deviation of 7.7 inches. This year Joey jumped 275 inches and his sister, Carla, jumped 207
inches. Both are State College students. Assume that male and female jumps are normally distributed.
Within their groups, which athlete had the more impressive performance? Explain briefly.
5.) The length of pregnancies from conception to natural birth among a certain female population is a
normally distributed random variable with mean 270 and standard deviation 10 days.
(a) What is the percent of pregnancies that last more than 300 days?
(b) How short must a pregnancy be in order to fall in the shortest 10% of all pregnancies?
6.) At summer camp, one of Megan‘s counselors told her that you can determine air temperature from the
number of cricket chirps.
(a) What is the explanatory variable, and what is the response variable?
(b) Megan collected data on temperature and number of chirps per minute on 12 occasions. She entered
the data into a statistical software package. Here are some of the results:
x = 166.8,
sx = 31.0
y = 78.83
sy = 9.11
r = 0.461
Use this information and your formula packet to determine the equation of the LSRL.
(c) One of Megan’s data points was recorded on a particularly hot day (93F). She counted 249 cricket
chirps in one minute. What temperature would Megan’s model predict for this number of cricket chirps?
(Round to the nearest degree.)
(d) What is the residual for the data point in part (c)?
e) Suppose that Megan counted 249 chirps on a day when the temperature was 55F. If this point were
the 13th data point, what effect, if any, would this 13th point have on Megan’s LSRL? Explain.
7.) In a study of the relationship between the amount of violence a person watches on TV and the
viewer’s age, 81 regular TV watchers were randomly selected and classified according to their age group
and whether they were a “low-violence” or “high violence” viewer. Here is a two-way table of the
results.
Age Group
16-34
35-54
55 & over
TOTALS
Amount of
Low
8
12
21
Violence
Watched
High
18
15
7
TOTALS
(a) Compute (in percents) the marginal distribution of age group for all people surveyed.
(b) Compute (in percents) the conditional distributions of age group among “low-violence” viewers.
Then do the same for “high-violence” viewers.
(c) Based on your answers in parts (a) and (b), Is there a relationship between age group and the amount
of violence watched on TV?
8.) The Earth’s Moon has many impact craters that were created when the inner solar system was
subjected to heavy bombardment of small celestial bodies. Scientists studied 11 impact craters on the
Moon to determine whether there was any relationship between the age of the craters (based on
radioactive dating of lunar rocks) and the impact rate (as deduced from the density of the craters) The
data are displayed in the scatterplot below.
(a) Describe the nature of the relationship between impact rate and age.
Prior to fitting a linear regression model, the researchers transformed both impact rate and age by using
logarithms. The following computer output and residual plot were produced.
(b) Interpret the value of r²
(c) Comment on the appropriateness of this linear regression for modeling the relationship between
transformed variables.
9.) Two pain relievers, A and B, are being compared for relief of postsurgical pain. Twenty different
strengths (doses in milligrams) of each drug were tested. Eight hundred postsurgical patients were
randomly divided into 40 different groups. Twenty groups were given drug A. Each group was given a
different strength. Similarly, the other twenty groups were given different strengths of drug B. Strengths
used ranged from 210 to 400 milligrams. Thirty minutes after receiving the drug, each patient was
asked to describe his or her pain relief on a scale of 0 (no decrease in pain) to 100 (pain totally gone).
The strength of the drug given in milligrams and the average pain rating for each group are shown
in the scatterplot below. Drug A is indicated with A's and drug B with B's.
(a) Based on the scatterplot, describe the effect of drug A and how it is related to strength in milligrams.
(b) Based on the scatterplot, describe the effect of drug B and how it is related to strength in milligrams.
(c) Which drug would you give and at what strength, if the goal is to get pain relief of at least 50 at the
lowest possible strength? Justify your answer based on the scatter-plot.
10.) As gasoline prices have increased in recent years, many drivers have expressed concern about the
taxes they pay on gasoline for their cars. In the United States, gasoline taxes are imposed by both the
federal government and by individual states. The boxplot below shows the distribution of the state
gasoline taxes, in cents per gallon, for all 50 states on January 1, 2006
(a) Based on the boxplot, what are the approximate values of the median and the interquartile range of the
distribution of state gasoline taxes, in cents per gallon? Mark and label the boxplot to indicate how you
found the approximated values
(b) The federal tax imposed on gasoline was 18.4 cents per gallon at the time the state taxes were in
effect. The federal gasoline tax was added to the state gasoline tax for each state to create a new
distribution of combined gasoline taxes. What are the approximate values, in cents per gallon, of the
median and interquartile range of the new distribution of combined gasoline taxes? Justify your answer.