AP Statistics
Practice Test Unit 3: Ch 7-10
Name______________________________________________
Part I - Multiple Choice (Questions 1-10: 2 pts each) - Circle the best answer.
1.
As reported in The New York Times (September 21, 1994, page C10), a study at the University of Toronto
determined that, for every 10 grams of saturated fat consumed per day, a woman’s risk of developing ovarian
cancer rises 20%. What is the meaning of the slope of the appropriate regression line?
a. Taking in 10 grams of fat results in a 20% increased risk of developing ovarian cancer.
b. Consuming 0 grams of fat per day results in a zero increase in the risk of developing ovarian cancer.
c. Consuming 50 grams of fat doubles the risk of developing ovarian cancer.
d. Increased intake of fat causes higher rates of developing ovarian cancer.
e. On average, women’s risk of developing ovarian cancer rises 2% for every gram of fat consumed per
day.
2.
The relationship between population (y) and year (x) was determined to be exponential. The least-squares
ˆ
regression equation of the appropriately transformed data was y  0.05  0.004 x . What would be the
predicted population in the year 1990?
a.
b.
c.
d.
e.
3.
8.01
288,403,150
3.21
102,329,299
There is insufficient information to make a prediction.
Which of the following statements about the correlation, r, are true?
I. A correlation of 0.2 means that 20% of the points are highly correlated.
II. The square of the correlation measures the proportion of the variability in the y-values that is accounted for by
the linear relationship with x.
III. Perfect correlation, that is, when the points lie exactly on a straight line, results in r =0.
a.
b.
c.
d.
e.
4.
I only
II only
III only
None of these statements true.
None of the above gives the complete set of true responses.
If every woman married a man who was exactly 2 inches taller than she, what would the correlation between the
heights of married men and women be?
a. Close to –1
b.
0
c. Positive, close to 0
d.
Close to 1
e. 1
5. Forty-five AP Students reported their hours of sleep per night. The mean was 7.3 and the standard deviation was
1.2. Which of the following correctly interprets these statistics?
a.
b.
c.
d.
e.
Nearly all students got between 6.1 and 8.5 hours of sleep per night.
The median must be above 7.3, due to the high standard deviation.
The typical deviation of the students’ sleep hours is about 1.2 from the mean.
Half of students sleep less than 7.3 hours.
At most 22 students sleep more than 7 hours per night.
6. A simple random sample of 35 world-ranked chess players provides the following statistics:
Number of hours of study per day: x  6.2, sx  1.3
Yearly winings: y  $208, 000, s y  $42, 000
Correlation r = 0.15
Based on this data, what is the resulting linear regression equation?
a. Winnings = 4850 Hours + 178,000
b. Winnings = 6300 Hours + 169,000
c. Winnings = 31,200 Hours + 14,550
d. Winnings = 32,300 Hours + 7750
e. Winnings = 42,000 Hours – 52,400
7. Which of the following would provide evidence that a power law model describes the relationship between a response variable y
and an explanatory variable x?
a.
b.
c.
d.
e.
A scatterplot of y versus x looks approximately linear.
A scatterplot of log y versus log x looks approximately linear.
A scatterplot of log y versus x looks approximately linear.
A scatterplot of y versus log x looks approximately linear.
A residual plot of y versus x looks approximately linear.
8. A researcher observes that, on average, the number of divorces in cities with major league baseball teams is larger than in
cities without major league baseball teams. The most plausible explanation for this observed association is that
a.
b.
c.
d.
e.
the presence of a major league baseball team causes the number of divorces to rise (perhaps husbands are spending too
much time at the ballpark).
the association is due to common response (major league teams tend to be in large cities with more people, thus a
greater number of divorces).
the high number of divorces is responsible for the presence of a major league baseball team (more single men means
potentially more fans at the ballpark, making it attractive for an owner to relocate to such cities).
the observed association is purely coincidental. It is implausible to believe the observed association could be anything
other than accidental.
the number of divorces is confounding the relationship between the size of cities and whether or not they have a
baseball team.
9. The weights of cockroaches living in a typical college dormitory are approximately normally distributed with a mean of
80 grams and a standard deviation of 3.5 grams. The percentage of cockroaches weighing between 77 grams and 83
grams is about:
a.
99.7%
b. 95.0%
c. 68.0%
d. 34.0%
e. 60.9%
10. Suppose that the scatterplot of (log x, log y) shows a linear relationship with strong, positive correlation close to 1.
Which of the following are true?
I.
II.
III.
The variables x and y also have a correlation close to 1.
A scatterplot of (x, y) shows a strong nonlinear pattern.
The residual plot of the variables x and y shows a random pattern.
a.
b.
c.
d.
e.
I only
II only
III only
I and II
I, II, and III
Part II – Free Response (Questions 11-14) – Show your work and explain your results clearly.
11. 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
above. (Free Response 2003 #1B)
The scatterplot displays the data that were collected from the
students.
(a) After point P, labeled on the graph above, was removed
from the data, a second linear regression
was performed and the computer output
is shown at right.
Does point P exercise 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 student
represented by P was recorded incorrectly. The corrected
data point for this student is represented by the letter Q in
the scatterplot at right.
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.
9
12. Animal-waste lagoons and spray fields near aquatic environments may significantly degrade water quality and
endanger health. The national Atmospheric Deposition Program has monitored the atmospheric ammonia at swine farms
since 1978. The data on the swine population size (in thousands) and atmospheric ammonia (in parts per million) for one
decade are given below. (Free Response 2002 #1B)
(a) Construct a scatterplot for these data.
(b) Find the LSRL.
yˆ  .133x  .127
(c) The value for the correlation coefficient for these data is 0.85. Interpret this value.
There is a strong, positive, linear relationship between swine population and atmospheric ammonia.
(d) Based on the scatterplot in part (a) and the value of the correlation coefficient in part (b), does it appear that the
amount of atmospheric ammonia is linearly related to the swine population size? What other information should you
consider?
Yes, r is close to 1, the scatter plot appears linear and the residual plot is scattered with no patterns or curves.
(e) What percent of the variability in atmospheric ammonia can be explained by swine population size?
R sqrd = .7225 so 72.25%
13. The following data represent the Woodward Academy Upper School enrollment over 35 years.
Year
Enrollment
(a)
1965
650
1970
690
1975
740
1980
790
1985
840
1990
900
1995
960
Determine an appropriate model for the data. Justify your answer. Let 1965 = year 65.
(x, logy)  r sqrd = .9998, the scattered plot appears to be linear and the residual plot is scattered.
(b)
Use your model to predict the enrollment in 2010. Comment on your result.
yˆ  10.0057 x 2.443
yˆ  1174.9
Be careful extrapolating, especially with time!
2000
1025