AP Statistics
8/31/06
Coley / P. Myers
Test #1 (Chapters 1-6)
Name ______________________________________________
Period ___________
Honor Pledge _________________________________________
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1. In order to rate TV shows, phone surveys are sometimes used. Such a survey might record several variables,
some of which are listed below. Which of these variables are categorical?
I.
II.
III.
IV.
V.
(a)
(b)
(c)
(d)
(e)
The type of show being watched
The number of persons watching the show
The ages of persons watching the show
The name of the show being watched
The number of times the show has been watched in the last month
II, III, and V
I only
I and V
I and IV
None of the above describes the complete set of correct responses
2. The stemplot displays the 1988 per capita income (in hundreds of dollars)
of the 50 states. Which of the following best describes the data?
(a)
(b)
(c)
(d)
(e)
Skewed distribution, mean greater than median
Skewed distribution, median greater than mean
Symmetric distribution, mean greater than median
Symmetric distribution, median greater than mean
Symmetric distribution with outliers on high end
3. A study was conducted on the weights of three different species
of fish (Bream, Perch & Roach) found in a lake in Finland. These
three fish (bream, perch and roach) are commercial fish. Their
weights are displayed in the boxplots. Which of the following
statements comparing these boxplots is NOT correct?
(a) The median weights of the three species differ.
(b) The spread of roach is less than the spread of the other two
species.
(c) The distributions of weights are approximately symmetric for all three species.
(d) There are no outliers in weight for the three species.
(e) The variability in the weights for the three species combined exceeds the variation in the medians of the three
species.
4. The mean age of 14 of the members attending a mathematics department faculty meeting is 42. Mr. Myers, who
is 57, arrives late. What is the average of all 15 members?
(a) 43
(b) 44
(c) 45
(d) 46
(e) cannot be determined
5. 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 4 grams. The percentage of cockroaches weighing between 77 grams
and 83 grams is about:
(a) 99.7%
(b) 95%
(c) 68%(d) 55%
(e) 34%
6. Scores on the American College Test (ACT) are normally distributed with a mean of 18 and a standard deviation
of 6. The interquartile range of the scores is approximately:
(a) 8.1
(b) 12
(c) 6
(d) 10.3 (e) 7
7. The test grades at a large school have an approximately normal distribution with a mean of 50. What is the
standard deviation of the data so that 80% of the students are within 12 points (above or below) the mean?
(a) 5.875
(b) 9.375
(c) 10.375
(d) 14.5 (e) cannot be determined from the given information
8. In the accompanying display, which has the larger mean and which has
the larger standard deviation?
(a) Larger mean, A; larger standard deviation, A
(b) Larger mean, A; larger standard deviation, B
(c) Larger mean, B; larger standard deviation, A
(d) Larger mean, B; larger standard deviation, B
(e) Larger mean, B; same standard deviation
9. You have a set of data that you suspect came from a normal distribution. In order to assess normality, you
construct a normal probability plot. Which of the following would constitute evidence that the data actually
came from a normal distribution?
(a)
(b)
(c)
(d)
(e)
A strongly linear relationship between the data and their standardized values.
A bell-shaped (normal) relationship between the data and their standardized values.
A random scattering of points when the standardized values are plotted against the data.
A strongly non-linear relationship (with no outliers) between the data and their percentiles.
A uniform relationship between the percentiles and the standardized values.
10. The cost of glass cleaner is nicely described by a Normal model with a mean cost per ounce of 7.7 cents with a
standard deviation of 2.5 cents. What is the z-score of Windex with a cost of 10.1 cents per ounce?
(a) 0.96
(b) 1.31
(c) 1.94
(d) 2.25
(e) 3.00
Part II – Free Response(Questions 11-13) – Show your work.
11. The heights of NCAA women basketball players are approximately normally distributed with
  2.5 .
  70 and
For each of the following, illustrate with a picture and evaluate.
(a) P(Height > 66)
(c) P(Height < 64)
__________
(b) P(72
__________
 Height  74)
__________
(d) The value of X if P(Height > X) = 0.215.
________
12. The summary statistics for the number of inches of rainfall in Los Angeles for 177 years, beginning in 1877,
are shown below.
N
117
Mean
14.941
Median
13.070
StDev
6.747
Min
4.850
Max
38.180
Q1
9.680
Q3
19.250
(a) Describe a procedure that uses these summary statistics to determine whether there are outliers.
(b) Are there outliers in these data? Justify your answer based on the procedure that you described in (a).
(c) The news media reported that in a particular year, there were only 10 inches of rainfall. Use the
information provided to comment on this reported statement.
13. Two parents have each built a toy catapult for use in a game at an elementary school fair. To play the game, the
students will attempt to launch Ping-Pong balls from the catapults so that the balls land within a 5-centimeter band.
A target line will be drawn through the middle of the band, as shown in the figure below. All points on the target
line are equidistant from the launching location.
If a ball lands within the shaded band, the student will win a prize.
The parents have constructed the two catapults according to slightly different plans. They want to test these
catapults before building additional ones. Under identical conditions, the parents launch 40 Ping-Pong balls from
each catapult and measure the distance that the ball travels before landing. Distances to the nearest centimeter
are graphed in the dotplot below.
(a) Comment on any similarities and any differences in the two distributions of distances traveled by balls launched
from catapult A and catapult B.
(b) If the parents want to maximize the probability of having the Ping-Pong balls land within the band, which one of
the catapults, A or B, would be better to use than the other? Justify your choice.
(c) Using the catapult that you chose in part (b), how many centimeters from the target line should this catapult be
placed? Explain why you chose this distance.
AP Statistics @ Woodward Academy
Thursday, September 21, 2006
Coley / P. Myers
Test #2 (Chapters 7-9)
Name _________________________________________
Period ______
Honor Pledge ___________________________________
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1. Given the least-squares regression line:
[Monopoly Property Cost = 67.3 + 6.78 * [Spaces From GO]
Determine the residual for Reading Railroad which costs $200 and is 5 spaces from GO.
(a)
(b)
(c)
(d)
(e)
–98.8
–9.88
98.8
–1418.3
A residual has no meaning since one of the variables is categorical.
2. The computer printout of the relationship between the number of hours studying and the number of hours
watching television is shown below.
Predictor
Constant
Television
Coef
5.1674
-0.56484
SE Coef
0.3203
0.07636
T
16.13
-7.40
P
0.000
0.000
S = 0.522956
R-Sq = 84.5%
R-Sq(adj) = 83.0%
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
10
11
MS
14.963
SS
14.963
2.735
17.698
F
54.71
P
0.000
0.273
What is the value of the correlation coefficient for the number of hours studying and the number of hours
watching television?
(a)
(b)
(c)
(d)
(e)
0.919
0.523
.830
-0.919
-0.565
3. Data are obtained for a group of college freshman examining their SAT scores (math plus verbal) from their
senior year of high school and their GPAs during their first year of college. The resulting regression equation is:
^
GPA  0.00161* SAT  1.35 with
s SAT
 120 , and sGPA  .3057
What percentage of the variation in GPAs can be explained by looking at SAT scores?
(a)
(b)
(c)
(d)
(e)
0.161%
16.1%
39.9%
63.2%
This value cannot be computed from the information given.
4.
Suppose the correlation between two variables is r = 0.23. What will the new correlation be if 0.14 is added to
all values of the x-variable, every value of the y-variable is doubled, and the two variables are interchanged?
(a)
(b)
(c)
(d)
(e)
0.23
0.37
0.74
-0.23
-0.74
5.
Which of the following characteristics of a least-squares regression equation is false?
(a)
(b)
(c)
(d)
(e)
The LSRL minimizes the sum of the residuals.
The average residual of a LSRL is 0.
The LSRL minimizes the sum of the squared residuals.
The slope of the LSRL is a constant multiple of the correlation coefficient.
The slope of the LSRL line tells you, on the average, how much the response variable will change for each unit
change in the explanatory variable.
6.
A study of the fuel economy for various automobiles plotted
the fuel consumption (in liters of gasoline used per 100
kilometers traveled) vs. speed (in kilometers per hour).
A least-squares regression line was fitted to the data and
residual plot is displayed to the right. What does the
pattern of the residuals tell you about the linear model?
the
(a) The evidence is inconclusive.
(b) The residual plot confirms the linearity of the data.
(c) The residual plot suggests a different line would be more
appropriate.
(d) The residual plot clearly contradicts the linearity of the
data.
(e) None of the above.
7.
With regard to regression, which of the following statements about outliers are true?
I.
II.
III.
(a)
(b)
(c)
(d)
(e)
Outliers have large residuals.
A point may not be an outlier even though its x-value is an outlier in the x-variable and its yvalue is an outlier in the y-variable.
Removal of an outlier sharply affects the regression line.
I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of true responses.
8.
As reported in the Journal of the American Medical Association (June 13, 1990), for a study of ten
nonagenarians, the following tabulation shows a measure of strength versus a measure of functional mobility
Strength
(kg)
Walk time
(s)
7.5
6
11.5
10.5
9.5
18
4
12
9
3
18
46
8
25
25
7
22
12
10
48
What does the slope of the least-squares regression line signify?
(a)
(b)
(c)
(d)
(e)
The sign is positive, signifying a direct cause-and-effect relationship between strength and mobility.
The sign is positive, signifying that the greater the strength, the greater the functional mobility.
The sign is negative, signifying that the relationship between strength and functional mobility is weak.
The sign is negative, signifying that the greater the strength, the less the functional mobility.
The slope is close to zero, signifying that the relationship between strength and functional mobility is weak.
9.
Some AP Statistics students were interested in finding out if there was a relationship between the number of
hours of study for a chapter test and the score on that test. On the basis of the number of hours their
classmates studied for the chapter 3 test and the scores on the test (out of 100%), the LSRL was
^
^
y  72.53  5.88 x , where x is the number of hours studied and y is the predicted score on the test. Which
statement correctly interprets the meaning of the slope of this regression line?
(a) For each additional hour studied, the predicted score on the test increases by approximately 73%.
(b) For each additional hour studied, the predicted score on the test increases by approximately 6%.
(c) For each additional percent of increase on the test, the predicted number of hours studied increases by
approximately 73%.
(d) For each additional percent of increase on the test, the predicted number of hours studied increases by
approximately 6%.
(e) We cannot use this regression equation, since cause-effect has not been proven.
10. Consider the three points (2,11), (3,17), (and (4,29). Given any straight line, we can calculate the sum of the
squares of the three vertical distances from these points to the line. What is the smallest possible value this
sum can be?
(a)
(b)
(c)
(d)
(e)
6
9
29
57
cannot be determined
Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.
11. Lydia and Bob were searching the Internet to find information on air travel in the United States. They found
data on the number of commercial aircraft flying in the United States during the years 1990-1998. The dates
were recorded as years since 1990. Thus, the year 1990 was recorded as year O. They fit a least squares
regression line to the data. The graph of the residuals and part of the computer output for their regression are
given below.
a.
Is a line an appropriate model to use for these data? What information tells you this?
b.
What is the value of the slope of the least squares regression line?
Interpret the slope in the context of this situation.
c.
What is the value of the intercept of the least squares regression line?
Interpret the intercept in the context of this situation.
d.
What is the predicted number of commercial aircraft flying in 1992?
e.
What was the actual number of commercial aircraft flying in 1992?
12. 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 regression was performed and part of the resulting computer printout is shown below.
Predictor
Coef
StDev
T
P
Constant
8.107
2.731
2.97
0.021
Work
0.4919
0.1950
2.52
0.040
S = 4.349
R-Sq = 47.6%
R-Sq (adj) = 40.1%
The scatterplot below displays the data that were collected from the 9 students.
Scatterplot of Study vs Work
P
25
Study
20
15
10
5
0
5
10
15
Work
20
25
30
(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.
Predictor
Coef
StDev
T
P
Constant
11.123
3.986
2.79
0.032
Work
0.1500
0.3834
0.39
0.709
S = 4.327
R-Sq = 2.5%
R-Sq (adj) = 0.0%
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 below.
Scatterplot of Study vs Work
17.5
Study
15.0
12.5
10.0
7.5
5.0
Q
0
5
10
15
Work
20
25
30
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.
AP Statistics @ Woodward Academy
Thursday, October 5, 2006
Coley / P. Myers
Test #3 (Chapters 1-10)
Name _________________________________________
Period ______
Honor Pledge ___________________________________
Part I - Multiple Choice (Questions 1-8) - Circle the answer of your choice.
1.
A response variable appears to be exponentially related to the explanatory variable. The natural logarithm of each y-value
is taken and the least-squares regression line is found to be
ln(y) = 1.64 – 0.88x. Rounded to two decimal places, what is the predicted value of y when x = 3.1?
(a)
(b)
(c)
(d)
(e)
-1.09
-0.34
0.34
0.082
1.09
2. The 5-number summary for a one-variable data set is {5, 18, 20, 40, 75}. If you wanted to construct a modified box-andwhiskers plot for the dataset (that is, one that shows outliers if there are any), what would be the maximum possible length of
the right side “whisker”?
(a)
(b)
(c)
(d)
(e)
35
33
5
55
53
3. Mary’s best time for downhill sking the challenging course has a z-score of 0.5 as compared to all skiers that are timed on the
same course. Which statement best interprets her z-score?
(a) Mary’s time is 0.5 seconds times faster than all skiers timed on the same course.
(b) Mary’s time is 0.5 seconds faster than all skiers timed on the same course.
(c) Mary’s time is 0.5 standard deviations below the mean time for all skiers timed on the same course.
(d) Mary’s time is 0.5 standard deviations above the mean for all skiers timed on the same course.
(e) Mary skis worse than the majority of the skiers timed on the same course.
4. The equation of a least-squares regression line is y = 3.34x – 7.012. One of the points in the scatter plot was (5,10). What is
the residual for this point?
(a)
(b)
(c)
(d)
(e)
-10.388
-0.312
0.312
9.688
10.388
5. The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2
inches. If Rachel is at the 99th percentile in height for adult women, then her height, in inches, is closest to
(a) 60
(b) 62
(c) 68
(d) 70
(e) 74
6. A set of data was re-expressed in two ways.
( x, y )  ( x, log( y ))
Model B: ( x, y )  (log( x), log( y ))
Model A:
Based on the residual plots shown below, which model would be more appropriate?
(a)
(b)
(c)
(d)
(e)
Model A because the residuals are reasonably random.
Model B because the residuals are reasonably random.
Model A because the residuals are decreasing.
Model B because the residuals show a pattern.
Cannot be determined.
7. If a least-squares residual plot appeared as in the enclosed graph, the appropriate model would be:
(a)
(b)
(c)
(d)
(e)
exponential model
linear model
power model
an undetermined non-linear model
square root model
8. A copy machine dealer has data on the number x of copy machines at each of 89 customer locations and the number y of
service calls in a month at each location.
x  8.4, s  2.1, y  14.2, s  3.8, r  0.86
x
y
Summary calculations give
.
About what percent of the variation in number of service calls is explained by the linear relation between number of service
calls and number of machines?
(a) 86%
(b) 93%
(c) 74%
(d) none of these
(e) cannot be determined
Part II – Free Response (Questions 9-11) – Show your work and explain your results clearly.
9. 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.
8000
7000
Impact Rate
6000
5000
4000
3000
2000
1000
0
0.4
0.9
1.4
Age
(a) Describe the nature of the relationship between age and impact rate.
Prior to fitting a linear regression model, the researchers transformed both impact rate and age by using logarithms. The
following computer printout and residual plot were produced.
Regression equation:
log(rate) = 4.82 - 3.92 log(age)
Predictor
Constant
log (age)
S = 0.5977
Coef
4.8247
-3.9232
SE Coef
0.1931
0.4514
R-Sq = 89.4%
T
24.98
-8.69
P
0.000
0.000
R-Sq(adj) = 88.2%
(b) Interpret the value of r2.
(c) Comment on the appropriateness of this linear regression for modeling the relationship between the transformed
variables.
10. A random sample of 400 married couples was selected from a large population of married couples.

Heights of married men are approximately normally distributed with mean 70 inches and standard deviation 3
inches.

Heights of married women are approximately normally distributed with mean 65 inches and standard deviation
2.5 inches.

There were 20 couples in which the wife was taller than her husband, and there were 380 couples in which the
wife was shorter than her husband.

The relationship between husband’s height vs. wife’s height for the 400 married couples was approximately
linear with correlation 0.4.
(a) Determine the boundary heights for the middle 95% of men’s heights.
(b) Determine the boundary heights for the middle 95% of women’s heights.
(c) Determine the equation of the least-squares regression line for the linear relationship between men’s heights and
women’s heights.
(d) Using all the information given and the results from parts (a), (b), and (c), sketch an oval that could enclose the points
on the scatterplot below.
100
90
80
70
60
50
40
30
20
10
10 20 30 40 50 60 70 80 90 100
11. A plot of the number of defective items produced during 20 consecutive days at a factory is shown below.
Scatterplot of Number of Defective Items vs Day Number
Number of Defective Items
5
4
3
2
1
0
5
10
Day Number
15
(a) Draw a histogram that shows the frequencies of the number of defective items.
(b) Give one fact that is obvious from the histogram but is not obvious from the scatterplot.
(c) Give one fact that is obvious from the scatterplot but is not obvious from the histogram.
20
AP Statistics
11/02/06
Coley / P. Myers
Test #4 (Chapters 11-13)
Name ____________________________________________________
Period ___________
Honor Pledge ______________________________________________
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1.
(a)
(b)
(c)
(d)
(e)
2.
(a)
(b)
(c)
(d)
(e)
3.
Who makes more mistakes on their income tax forms: accountants or taxpayers who prepare the forms themselves? A
random sample of income tax forms that were prepared by accounts was drawn form IRS records. An equal number of
forms that were self-prepared by taxpayers was also drawn. The average number of errors per form was compared to
determine if one group tends to make more mistakes than the other. What type of study is this?
census
experiment
voluntary response survey
observational study
matched-pairs study
A dance club holds a raffle at the end of each dance. Five dancers are selected at random to each draw one numbered
tag from a hat without replacement. There are 50 tags in the hat numbered from 1 to 50. Drawing a tag numbered
from 1 through 5 wins $20, tags 6 through 25 wins $10, and tags 26 through 50 wins $5. In order to determine the
average amount of money paid out, a simulation will be conducted using a random number table. Which of the following
assignments of random numbers to tag values is most appropriate for the simulation?
Using single-digit numbers, assign 0 to represent a $20 prize, 1-4 to represent a $10 prize, and 5-9 to be a $5 prize.
Using single-digit numbers, assign 0 to represent a $20 prize, 1 to represent a $10 prize, and 2 to represent a $5 prize.
Numbers 3-9 are ignored.
Using two-digit numbers, assign 20 to represent a $20 prize, 10 to represent a $10 prize, and 05 to represent a $5
prize. Numbers 00-04, 06-09, 11-19, 21-99 are ignored.
Using two-digit numbers, assign 01-05 to represent a $20 prize, 06-25 to represent a $10 prize, and 26-50 to
represent a $5 prize. Numbers 51-99 and 00 are ignored.
Using two-digit numbers, assign 01-10 to represent a $20 prize, 11-40 to represent a $10 prize, and 41-99 and 00 to
represent a $5 prize.
(a)
(b)
(c)
(d)
(e)
The student council wants to survey their students to see what brands of soft drinks they want in the school machines.
They randomly sampled 30 freshmen, 30 sophomores, 30 juniors, and 30 seniors. The sampling method they used is a:
simple random sample
stratified random sample
cluster sample
systematic random sample
convenience sample
4.
(a)
(b)
(c)
(d)
(e)
What is the major difference between an experiment and an observational study?
A treatment is imposed in an experiment.
An observational study can establish cause-effect relationships.
There are two control groups instead of one in an experiment.
Observational studies use only one population.
Experiments are blinded.
5.
(a)
(b)
(c)
(d)
(e)
A simple random sample of size n is selected in such a way that:
Each member of the population has an equal chance of being selected.
Each member of the population is given an opportunity to respond to the survey.
All samples of size n have the same chance of being selected.
The probability of selecting any sample is known to be 1/n.
The sample is guaranteed to represent the entire population.
6.
In sample surveys, bias can be controlled by all of the following except:
Using a random sampling procedure.
Wording questions so they are not confusing or misleading.
Carefully training and supervising interviewers.
Prompting respondents so that they give correct responses.
Reducing non-response and undercoverage.
(a)
(b)
(c)
(d)
(e)
7.
A new medication has been developed to cure a certain disease. The disease progresses in three stages: I, II, and III,
each progressively worse than the one before it. Ninety volunteers are gathered to test the new medication, 30 in each
of the three stages. The medication will be administered to subjects daily in one of three dosages: 100 mg for each
subject in stage I, 200 mg for each subject in stage II, 300 mg for each subject in stage III. After 8 weeks, the
proportion of subjects cured of the disease will be recorded. Why is this NOT a good experimental design?
I.
II.
III.
Because experiments of this type should only use one dosage level of medication.
Because disease stage is potentially confounded with dosage level.
Because the experiment lacks a control group.
(a)
(b)
(c)
(d)
(e)
I only
II only
I and II only
II and III only
I, II, and III
8.
A garage door manufacturer has developed a new type of door for houses in the Southeast part of the United States.
Doors in this area of the country are particularly susceptible to damage from salty ocean spray and the sun’s rays,
which tend to shine mainly on the north side of the house. An experiment will test the new type of garage door against
the existing type of door on eight houses in a particular residential area. An overhead view of the area is shown below.
The location of the garage door on each house is marked with an “X”.
Which of the following blocking schemes is
most appropriate to account for variables in
this study other than type of door?
(a) Form the houses into two blocks: {1,2,3,4}
and {5,6,7,8}
(b) Form the houses into two blocks: {1,3,5,7}
and {2,4,6,8}
(c) Form the houses into four blocks: {1,5},
{2,6}, {3,7} and {4,8}
(d) Form the houses into four blocks: {1,3},
{2,4}, {5,7} and {6,8}
(e) No blocking is necessary in this
experiment.
9. Five homes from a subdivision will be randomly selected to receive 1 month of free cable TV. There are 80 homes in the
subdivision. The homes are assigned numbers 01-80 and the random number table below (beginning with the first line and
reading from left to right) is used to select the five homes. No home may receive more than one free month of service.
Which of the following is a correct selection of the five homes?
99154
92210
(a) 9, 1, 5, 4, 7
(b) 15, 47, 03, 23, 23
(c) 15, 47, 03, 23, 35
(d) 99, 70, 23, 92, 08
(e) 99, 15, 47, 03, 92
70392
70439
23889
08629
92335
73299
10. A graduate student designed a study to determine whether a new activity-based method is better than the traditional
lecture of teaching statistics. He found two teachers to help him in his study for one semester. Mr. Dull volunteered to
continue teaching with traditional lectures and Ms. Perky agreed to try the new activity-based method. Each teacher
planned to teach two sections of approximately forty students each for adequate replication. At the end of the semester,
all sections would take the same final exam and their scores would be compared. What is the explanatory variable in this
study?
(a) Teacher
(b) Section of the Course
(c) Teaching Method
(d) Final Exam Score
(e) Student
Part II – Free Response (Questions 11-13) – Show your work and explain your results clearly.
11. It rains on Paradise Island on 40% of the days. The chance of rain is independent from day to day. A travel agent is
signing people up to go on a 5-day tour of the island. She wants to know the chance of getting at least two consecutive days
of rain at any time during the 5 days. To determine this, a simulation will be used.
(a) Describe how you would use a random digit table to simulate whether at least two consecutive fays of rain occur over a
5-day period.
(b) Conduct 10 trials of your simulation using the random number table below. By marking directly on or above the table,
make your procedure clear enough for someone to understand.
00233
54830
39108
57935
28715
08996
19223
39280
22222
31405
71405
49953
30324
80154
39490
96080
51290
33843
62322
80262
12. A biologist is interested in studying the effect of growth-enhancing nutrients and different salinity (salt) levels in water
on the growth of shrimps. The biologist has ordered a large shipment of young tiger shrimps from a supply house for use in
the study. The experiment is to be conducted in a laboratory where 10 tiger shrimps are placed randomly into each of 12
similar tanks in a controlled environment. The biologist is planning to use 3 different growth-enhancing nutrients (A, B, and
C) and two different salinity levels (low and high).
(a) List the treatments that the biologist plans to use in this experiment.
(b) Give one statistical advantage to having only tiger shrimps in the experiment. Explain why this is an advantage.
(c) Give one statistical disadvantage to having only tiger shrimps in the experiment. Explain why this is a disadvantage.
(d) Using the treatment listed in part (a), describe a completely randomized design that will allow the biologist to compare
the shrimps’ growth after 3 weeks.
13. The administrators in a high school are thinking of changing the school’s parking policy effective 3 weeks after school
begins. The administration has asked the student council to conduct a survey during the first week of school to determine
what students who won cars think about the proposal.
The student body has the following distribution. The number of students who won cars is also provided.
Grade
Population
Own Cars
Freshmen
500
0
Sophomores
550
180
Juniors
500
315
Seniors
450
405
The student council has decided to survey 100 students. The student body president wants to conduct a simple random
sample to obtain the names of 100 students to be surveyed. The student body secretary wants to use a stratified random
sample to obtain the names of the 100 students.
(a) If the student body president’s plan is chosen, describe the procedure used to select the 100 students.
(b) Describe one disadvantage of using the student body president’s plan.
(c) If the student body secretary’s plan is chosen, describe the procedure used to select the 100 students.
AP Statistics @ Woodward Academy
Tuesday, November 14, 2006
Coley / P. Myers
Test #3 (Chapters 14-15)
Name _________________________________________
Period ______
Honor Pledge ___________________________________
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1.
Suppose on any given day at school 0.15 of the English classes go to the computer lab, 0.10 of the Science
classes go to the computer lab, and 0.04 of English and Science classes go to the computer lab. What is the
probability that either an English or Science class will go to the computer lab?
(a) 0.15
(b) 0.19
(c) 0.21
(d) 0.25
(e) 0.29
2. Alex, Bryan, and Charlie are all playing tennis matches in a tournament against different opponents. Based
on previous performances, there is a 0.4 probability that Alex will win his first match, a 0.3 probability that
Bryan will win his first match, and a 0.2 probability that Charlie will win his first match. If the chance that
each wins his first match is independent of the others, what is the probability that none of them wins in
their first matches?
(a) 0.024
(b) 0.304
(c) 0.336
(d) 0.700
(e) 0.900
3. The 2000 Census identified the ethnic breakdown of the state of California to be approximately as follows:
White – 46%, Latino – 32%, Asian – 11%, Black – 7%, Other – 4%. Assuming that these are mutually
exclusive categories, what is the probability that a randomly selected person from the state of California is
of Asian or Latino descent?
(a) 46%
(b) 32%
(c) 11%
(d) 43%
(e) 3.5%
4. Given two events, A and B, if P(A) = 0.43, P(B) = 0.26, and P(A or B) = 0.68, then the two events are
(a) disjoint but not independent
(b) independent but not disjoint
(c) disjoint and independent
(d) neither disjoint nor independent
(e) not enough information is given to determine whether A and B are disjoint or independent
5. A dormitory on campus houses 200 students. Of the 200 students, 120 are male, 50 are seniors, and 40 are
male seniors. A student is selected at random. The probability of selecting a non-senior, given the student is a
female, is:
(a) 7/8
(b) 7/15
(c) 7/15
(d) 1/4
(e) 2/5
6. In an effort to get at the source of an outbreak of Legionnaire's disease at the 1979 APHA convention, a
team of epidemiologists carried out a case-control study involving all 50 cases and a sample of 200 non-cases
out of the 4000 persons attending the convention. Among the results, it was found that 40% of the cases went
to a cocktail party given by a large drug company on the second night of the convention, whereas 10% of the
controls attended the same party. Which of the following statements is appropriate for describing the 40% of
cases who went to the party? (C = case, P = attended party)
(a) P (C|P) = .40
(b) P (P|CC) = .40
(c) P (C|PC) = .40
(d) P (PC|C) = .40
(e) none of these
7. P(X) = 0.23 and P(X and Y) = 0.12 and P(X or Y) = .34, find P(YC).
(a) 0.23
(b) 0.52
(c) 0.11
(d) 0.77
(e) 0.48
8. Which of the following statements must be true?
(a)
(b)
(c)
(d)
(e)
If two
If two
If two
If two
If two
events are independent, they must be disjoint.
events are dependent, they must be disjoint.
events are disjoint, they must be independent.
events are not disjoint, they must be independent.
events are disjoint, they must be dependent.
9. For any two events A and B, which of the following statements must be true?
I.
II.
III.
IV.
V.
(a)
(b)
(c)
(d)
(e)
P(A) + P(B) = 1
P(A) + P(AC) = 1
P(A|B) + P(B|A) = 1
P(A|B) + P(AC|B) = 1
P(A|B) + P(A|BC) = 1
II and IV only
I and II only
II, II, and IV only
II and V only
None of the above describes the complete set of true statements.
Cause of Death
10. The cause of death and the age of the deceased are recorded for 440 patients from a hospital.
Accident
Homicide
Heart Disease
HIV
Cancer
Other
15-24
14
5
1
0
2
3
25-34
12
4
3
3
4
7
Age
35-44
15
3
14
6
17
16
45-54
12
0
34
4
47
26
55-64
7
0
63
0
89
43
If a person is known to be between the ages of 45 and 54, what is the probability that they died as a result of an
accident?
(a) 0.0273
(b) 0.0976
(c) 0.1364
(d) 0.2000
(e) 0.4878
Part II – Free Response (Questions 11-13) – Show your work and explain your results clearly.
11. The WA upper school student body consists of 55% females. Of the females, 65% like chicken fingers; of the
males, 85% like chicken fingers.
(a) Assign variable names to each of the unique events and describe the given probabilities using appropriate
probability notation.
(b) Set up an appropriately labeled diagram that describes this situation.
(c) If a student is randomly selected and they like chicken fingers, find the probability that the student is male.
Show your work.
12. Among the students in the WA upper school student body, 50% drive to school, 20% have a part-time job, and
40% neither drive to school nor have a part-time job.
(a) Assign variable names to each of the unique events and describe the given probabilities using appropriate
probability notation.
(b) Set up an appropriately labeled diagram that describes this situation.
(c) Are the events “Driving to School” and “Having a Part-Time Job” independent? Show your work.
13. The graph displays the scores of 32 students on a recent exam. The scores ranged from 64 to 95 points.
(a) Describe the shape of the distribution.
6
6
7
7
8
8
9
9
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
* * *
* * * *
*
(b) In order to motivate her students, the instructor wants to report that the overall class performance on the
exam was high. Which summary statistic, the mean or the median, should the instructor use to report that
overall exam performance was high? Explain.
(c) The midrange is defined by
minimum + maximum
. Compute this value using the exam data.
2
(d) Is the midrange a measure of center or a measure of spread? Explain.
AP Statistics @ Woodward Academy
Tuesday, November 21, 2006
Coley / P. Myers
Test #6 (Chapters 16)
Name _________________________________________
Period ______
Honor Pledge ___________________________________
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
1.
(a)
(b)
(c)
(d)
(e)
Family size can be represented by the random variable X. Determine the mean family size.
X
2
3
4
5
P(X)
.17
.47
.26
.10
2.94
3.00
3.29
3.49
3.86
2. The heights of married men are approximately normally distributed with a mean of 70 and a standard deviation of 3, while
the heights of married women are approximately normally distributed with a mean of 65 and a standard deviation of 2.5. If the
heights of married men & married women are independent, determine the probability that a randomly selected married woman is
taller than a randomly selected married man.
(a)
(b)
(c)
(d)
(e)
0.05
0.10
0.15
0.20
Cannot be determined from the given information.
3.
Which of the following is not true concerning discrete probability distribution?
(f)
(g)
(h)
(i)
(j)
The probability of any specific value is between 0 and 1, inclusive.
The mean of the distribution is between the smallest and largest value in the distribution.
The sum of all probabilities is 1.
The standard deviation of the distribution is between –1 and 1.
The distribution may be displayed using a probability histogram.
4.
A high school golf team of five players is to be in an upcoming tournament. Each of the players on the team will play a round
of golf and the team score is the sum of the five individual scores. The individual player scores are independent of each
other and approximately normally distributed with the following means and standard deviations.
Golfer
1
Mean
78
Standard Deviation 3
What are the mean and standard deviation of the team score?
(f)
(g)
(h)
(i)
(j)
2
79
4
3
81
2
4
84
4
5
93
6
Mean = 83, standard deviation = 3.8
Mean = 83, standard deviation = 9
Mean = 415, standard deviation = 6
Mean = 415, standard deviation = 9
Mean = 415, standard deviation = 19
5. A married couple decides they wish to start a family and they really want to have a baby girl. Because of financial
considerations, they decide they will have children until they have a girl or a total of 4 children. If the probability of having a
boy or girl is equally likely, determine the expected number of boys.
(f) 0.75
(g) 0.875
(h) 0.9375
(i) 1
(j) 1.25
6. A rock concert producer has scheduled an outdoor concert. If it is warm that day, she expects to make a $20,000 profit. If
it is cool that day, she expects to make a $5,000 profit. If it is very cold that day, she expects to suffer a $12,000 loss. Based
upon historical records, the weather office has estimated the chances of a warm day to be 0.60; the chances of a cool day to be
0.25. What is the producer's expected profit?
(a)
(b)
(c)
(d)
(e)
$5,000
$13,000
$15,050
$13,250
$11,450
7. The scores on the Woodward Academy AP Stat Test #1 (T1) had a mean of 27 with a standard deviation of 3 and the scores
on Test #2 (T2) had a mean of 29 with a standard deviation of 4. To reflect the true brilliance of the students taking the
course, he total score had to be adjusted according to the following definition: Total = 2*T1+3*T2 . What is the mean and
standard of Total?
(f)   141,   13.4
(g)   141,   18
(h)   141,   13.4
(i)   141,   13.4
(j) cannot be determined
Use the following information for questions 8-10. The independent random variables X and Y are defined by the following
probability distribution tables.
X
P(X)
1
.6
3
.3
6
.1
8. Determine the mean of X+Y
(f) 7.2
(g) 8.4
(h) 5.1
(i) 9
(j) 4.3
9. Determine the standard deviation of 3Y + 5
(f)
(g)
(h)
(i)
(j)
.44
3.62
0
5.1
5.44
10. Determine the standard deviation of 4X - 5Y.
(a)
(b)
(c)
(d)
(e)
15.38
–2.76
11.05
10.62
cannot be determined from the given information
Y
P(Y)
2
.1
3
.2
5
.3
7
.4
Part II – Free Response (Questions 11-13) – Show your work and explain your results clearly.
11. The depth from the surface of the earth to a refracting layer beneath the surface can be estimated using methods
developed by seismologists. One method is based on the time required for vibrations to travel from a distant explosion to a
receiving point. The depth measurement (M) is the sum of the true depth (D) and the random measurement error (E). That is M
= D + E. The measurement error (E) is assumed to be normally distributed with mean 0 feet and standard deviation 1.5 feet.
(a) If the true depth at a certain point is 2 feet, what is the probability that the depth measurement will be negative?
(b) Suppose three independent depth measurements are taken at the point where the true depth is 2 feet. What is the
probability that at least one of these measurements will be negative?
(c) What is the probability that the mean of the three independent depth measurements taken at the point where the true
depth is 2 feet will be negative?
12. Two antibiotics are available as treatment for a common ear infection in children.


Antibiotic A is known to effectively cure the infection 60 percent of the time. Treatment with antibiotic A
costs $50.
Antibiotic B is known to effectively cure the infection 90 percent of the time. Treatment with antibiotic A
costs $80.
The antibiotics work independently of one another. Both antibiotics can be safely administered to children. A health insurance
company intends to recommend one of the following two plans of treatment for children with this ear infection.


Plan I: Treat with antibiotic A first. If it is not effective, then treat with antibiotic B.
Plan II: Treat with antibiotic B first. If it is not effective, then treat with antibiotic A.
(a) If a doctor treats a child with an ear infection using Plan I, what is the probability that the child will be cured?
If a doctor treats a child with an ear infection using Plan II, what is the probability that the child will be cured?
(b) Compute the expected cost per child when plan I is used for treatment.
Compute the expected cost per child when plan II is used for treatment.
(c) Based on the results in parts (a) and (b), which plan would you recommend?
Explain your recommendation.
13. John believes that as he increases his walking speed, his pulse rate will increase. He wants to model this relationship. John
records his pulse rate, in beats per minute (pbm), while walking at each of seven different speeds, in miles per hour (mph). A
scatterplot and regression output are shown below.
(a) Using the regression output, write the equation of the fitted regression line.
(b) Estimate John’s pulse rate if he walks at 2 mph.
(c) Note that S = 3.087. Interpret this value in the context of this study.
(d) Explain the meaning of R-Sq in the context of this study.
11. A department supervisor is considering purchasing one of two comparable photocopy machines, A or B. Machine A costs
$10,000 and Machine B costs $10,500. This department replaces photocopy machines every three years. The repair contract
for Machine A costs $50 per month and covers an unlimited number of repairs. The repair contract for Machine B costs $200
per repair. Based on past performance, the distribution of the number of repairs needed over any one-year period for Machine
B is shown below.
Number of Repairs
Probability
0
0.50
1
0.25
2
0.15
3
0.10
You are asked to give an overall recommendation based on overall cost as to which machine, A or B, along with its repair contract,
should be purchased. What would your recommendation be? Give a statistical justification to support your recommendation.
11. For an upcoming concert, each customer may purchase up to 3 child tickets and 3 adult tickets. Let C be the number of child
tickets purchased by a single customer. The probability distribution of the number of child tickets purchased by a single
customer is given in the table below.
C
P(C)
0
0.4
1
0.3
2
0.2
3
0.1
(a) Compute the mean and the standard deviation of C.
(b) Suppose the mean and the standard deviation of the number of adult tickets purchased by a single customer are 2 and
1.2, respectively. Assume that the number of child tickets and the number of adult tickets purchased are independent
random variables. Compute the mean and the standard deviation of the total number of adult and child tickets
purchased by a single customer.
(c) Suppose each child ticket costs $15 and each adult ticket costs $25. Compute the mean and the standard deviation of
the total amount spent per purchase.
AP Statistics
12/5/06
Coley / P. Myers
Test #7 (Chapter 17)
Name ____________________________________________________
Period ___________
Honor Pledge ______________________________________________
Part I - Multiple Choice (Questions 1-10) - Circle the answer of your choice.
5. Sixty-five percent of all divorce cases cite incompatibility as the underlying reason. If four couples file for a
divorce, what is the probability that exactly two will state incompatibility as the reason?
(f)
(g)
(h)
(i)
(j)
.104.
.207
.254
.311
.423
6. Which
I.
II.
III.
(f)
(g)
(h)
(i)
(j)
of the following are true statements?
The histogram of a binomial distribution with p = .5 is always symmetric.
The histogram of a binomial distribution with p = .9 is skewed to the right.
The histogram of a geometric distribution with p = .3 is always skewed right.
I and II
I and III
II and III
I, II, and III
None of the above gives the complete set of complete responses.
3. Binomial and geometric probability situations share many conditions. Identify the choice that is not shared.
(k)
(l)
(m)
(n)
(o)
The probability of success on each trial is the same.
There are only two outcomes on each trial.
The random variable is the number of successes in a given number of trials.
The probability of a success equals 1 minus the probability of a failure.
The mean depends on the probability of a success.
4. An inspection procedure at a manufacturing plant involves picking thirty items at random and then accepting the
whole lot if at least twenty-five of the thirty items are in perfect condition. If in reality 85% of the whole lot is
perfect, what is the probability that the lot will be accepted?
(k)
(l)
(m)
(n)
(o)
.524
.667
.186
.476
.711
5. A recent study of the WA Upper School student body determined that 41% of the students were “chic”. If Mr.
Floyd has developed a test for “chic-ness”, what is the average number of students we would need to test in
order to find one who is “chic”?
(k)
(l)
(m)
(n)
(o)
2
2.43
3
3.57
1, because the study is clearly in error since all WA students are “chic”
6. A student is randomly generating 1-digit numbers on his TI-84. What is the probability that the first four that
appears will be the 8th digit generated?
(k)
(l)
(m)
(n)
(o)
.053
.082
.048
.742
.500
7. 3,600,000 dice are rolled. Determine the probability that between 599,000 and 610,000 4’s appear.
(k)
(l)
(m)
(n)
(o)
0.67
0.74
0.92
0.08
ERR:DOMAIN
8. A probability experiment involves a series of identical, independent trials with two outcomes (success/failure)
per trial and the probability of a success on each trial is 0.1. Determine the number of trials, n, in a binomial
experiment such that the expected number of successes in that binomial experiment will be equal to the expected
number of trials in a geometric experiment.
(b)
(c)
(d)
(e)
(f)
2
5
10
50
100
9. In which of the following games would you have the best chance of winning?
(f)
(g)
(h)
(i)
(j)
Toss a coin 20 times. You win if you get more than 11 heads.
Toss a coin 10 times. You win if you don’t get 4, 5, or 6 heads.
Toss a coin 7 times. You win if you get at least 5 heads.
Toss a coin 4 times. You win if you get at least 3 heads.
Toss a coin 5 times. You win if you get exactly 3 heads.
10. The renowned soccer player, Levi Gupta scores a goal on 30% of his attempts. The random variable X is defined
as the number of goals scored on 50 attempts.
The renowned gambler, Mohammed Smith, wins at Blackjack 25% of the time. The random variable Y is defined
as the number of games needed to win his first game.
Define the random variable Z as the total number of soccer goals scored and blackjack games played. Determine
the mean and standard deviation of the random variable Z.
(k)
(l)
(m)
(n)
(o)
11, 6.7
19, 6.7
11, 4.74
19, 4.74
Cannot be determined with the given information.
Part II – Free Response (Questions 11-12) – Show your work and explain your results clearly.
11. Sophie, Ms. Coley’s favorite dog, loves to play catch. Unfortunately, she (Sophie, not Ms. Coley) is not
particularly adept at catching as her probability of catching the ball is 0.15.
(a) Ms. Coley is interested in determining how many tosses it will take for Sophie to catch the ball once.
(i) Can this situation be described as binomial, geometric, or neither? Explain.
(ii) What is the expected number of tosses it will take for Sophie to catch the ball once?
(iii) What is the probability it will take exactly 10 tosses in order for Sophie to catch the ball?
(b) Mr. Wylder, avid baseball player & coach, decides to train Sophie. After three-a-day training sessions for 4
weeks, the probability that Sophie catches the ball has increased to 0.35. Mr. Wylder is interested in
determining the number of times Sophie will catch the ball in 25 tosses.
(i)
Can this situation be described as binomial, geometric, or neither? Explain.
(ii)
What is the expected number of times that Sophie will catch the ball?
(iii)
What is the probability that Sophie will catch the ball 8 times in 25 tosses?
(c) Mr. Myers, knowing that Sophie is a reasonably smart dog and her probability of catching the ball will
actually improve 0.01 after each toss. Mr. Myers would like to find out the number of tosses required for
Sophie to catch the ball three times.
(i) Can this situation be described as binomial, geometric, or neither? Explain.
(ii) If Sophie’s initial probability of catching the ball is 0.15, what is the probability that it will take five tosses for
Sophie to catch the ball three times?
12. When a tractor pulls a plow through an agricultural field, the energy to pull that plow is called the draft. The
draft is affected by environmental conditions such as soil type, terrain, and moisture.
A study was done to determine whether a newly developed hitch would be able to reduce draft compared to the
standard hitch. (A hitch is used to connect the plow to the tractor.) Two large plots of land were used in this
study. It was randomly determined which plot was to be plowed using the standard hitch. As the tractor plowed
that plot, a measurement device on the tractor automatically recorded the draft at 25 randomly selected points in
the plot.
After the plot was plowed, the hitch was changed from the standard one to the new one, a process that takes a
substantial amount of time. Then the second plot was plowed using the new hitch. Twenty-five measurements of
draft were also recorded at randomly selected points in this plot.
(a) What was the response variable in this study?
Identify the treatments.
What were the experimental units?
(b) Given that the goal of the study was to determine whether a newly develop hitch reduces draft compared to
the standard hitch, was randomization properly used in this study? Justify your answer.
(c) Given that the goal of the study was to determine whether a newly develop hitch reduces draft compared to
the standard hitch, was replication properly used in this study? Justify your answer.
(d) Plot of land is a confounding variable in this study. Explain why.