Name:________________________
Period_____
AP Statistics Experiments, Surveys, Samples TEST
Part I: Multiple Choice. (2 points each)
Hand write the letter corresponding to the best answer in space provided on page 6.
_____1. Which one of the following is not a principle of experimentation?
(a) Randomly allocating experimental units to treatments.
(b) Stratifying the experimental units into groups of similar individuals and applying different
treatments to each stratum.
(c) Using double blindness to eliminate bias.
(d) Replicating to measure overall experimental error and increase precision.
(e) Using a control group to determine whether treatment really works.
_____2. A simple random sample of size n is selected in such a way that
(a)
(b)
(c)
(d)
(e)
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 7  rand .
The sample is guaranteed to represent the entire population.
_____3. In sample surveys, bias can be controlled by all of the following except
(a)
(b)
(c)
(d)
(e)
Using a probability or chance 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.
_____4. In a study on the effect of reinforcement on learning from programmed text, two experimental
treatments are planned: reinforcement given after every frame of programmed text or reinforcement
given after every three frames. Which one of the following control groups would serve best in this
study?
(a) A group which does not read the programmed text material.
(b) A group that reads the programmed material in prose formats.
(c) A group which reads the programmed material but does not receive reinforcement.
(d) A group that reads the programmed text material and reinforcement is given at random.
(e) A group which watches the video of the programmed material.
_____5. We say that the design of a study is biased if which of the following is true?
(a)
(b)
(c)
(d)
(e)
A racial or sexual preference is suspected.
Random placebos have been used.
The research designer has received a grant from a special interest group.
The correlation if greater than 1 or less than –1.
Certain outcomes are systematically favored.
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_____6. A graduate student did 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 treatment variable in this study?
(a) Teacher
(b) Section of the Course
(c) Teaching Method
(d) Final Exam Score
(e) Student
_____7. Which of the following are true statements?
I.
Voluntary response samples often underrepresent people with strong opinions.
II.
Convenience samples often lead to undercoverage bias.
III.
Questionnaires with nonneutral wording are likely to have response bias.
(a)
(b)
(c)
(d)
(e)
I and II
I and III
II and III
I, II, and III
None of the above gives the true set of responses.
_____ 8. What fault do all these sampling designs have in common?
I.
The Wall Street Journal plans to make a prediction for a presidential election based on a
survey of its readers.
II.
A radio talk show asks people to phone in their views on whether the United States should
pay off its huge debt to the United Nations.
III.
A police detective interested in determining a sample of high school students and interviews
each one about any illegal drug use by the student during the past year.
(a)
(b)
(c)
(d)
(e)
All the designs make improper use of stratification.
All the designs have errors that can lead to strong bias.
All the designs confuse association with cause and effect.
None of the designs satisfactorily controls for sampling error.
None of the designs makes use of chance in selecting a sample.
_____9. To survey the opinions of bleacher fans at Wrigley Field, a surveyor plans to select every onehundredth fan entering the bleachers one afternoon. Will this result in a random sample?
(a)
(b)
(c)
(d)
Yes, because each bleacher fan has the same chance of being selected.
Yes, but only if there is a single entrance to the bleachers.
Yes, because the 99 out of 100 bleacher fans that are not selected will form a control group.
Yes, because this is an example of systematic sampling, which is a special case of random
sampling.
(e) No, because each fan does not have the same chance of being selected.
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Use the following information to answer questions 10-12.
A personnel director at a large company studied the eating habits of employees by watching the
movement of a selected group of employees at lunchtime. The purpose of the study was to determine
the proportion of employees who buy lunch in the cafeteria, bring their own lunches, or go out to lunch.
_____10. The study would best be categorized as:
(a) A census
(b) A survey sample
(c) An observational study
(d) A designed experiment
(e) None of these
_____11. If the director includes only the employees in one department in her study, she is performing a
(a) Simple random sample
(b) Quota sample
(c) Convenience sample
(d) Multi-stage random sample
(e) Census
_____12. If the director selects 50 employees at random throughout the company and categorizes their
lunchtime practices by gender, she is:
(a) Blocking for gender
(b) Testing for a lurking variable
(c) Promoting sexual harassment
(d) Testing for bias
(e) None of these
_____13. A researcher wishes to determine if watching 4 or more hours of TV per day adversely affects
high school students’ academic performance. Which of the following designs is best?
(a)
(b)
(c)
(d)
Study the records of randomly selected students
Interview randomly selected students on their grades and TV habits
Monitor the grades and TV habits of randomly selected students
Monitor the grades of students randomly placed into an under four-hour TV group and an over
four-hour TV group
(e) Monitor the grades of students randomly placed into an under four-hour TV group, an over fourhour TV group and a no TV group
_____14. Which of the following is not a valid sample design?
(a) Code every member of a population and select 100 randomly chosen members
(b) Divide a population by gender and select 50 individuals from each group
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(c) Select individuals randomly and place into gender groups until you have the same proportion in
the groups as in the population
(d) Select five homerooms at random from all of the homerooms in a large high school
(e) All of these are valid
Use the following excerpt from the random digit table to answer questions 15-17.
21052 65031 45074 92846 67815
78231 01548 20235 56410 82713
_____15. Which of the following statements regarding this excerpt of given random digits is true?
(a) The table can only be used for data coded with five-digit numbers.
(b) In order to use this table for a population of 100 names, the names could be coded 00 to 99; then
distinct two-digit numbers would be selected sequentially to identify chosen names.
(c) It is critical to begin the selection of random digits at the beginning of the list.
(d) This table can only be used if the data labels include all of the digits in the table.
(e) None of these statements is true.
_____16. If data are labeled: 1. Chevy; 2. Plymouth; 3. Lincoln;4. Volkswagen; 5. Porsche; 6. Ford; and
single-digit random digit selection begins at the left side of the first row, which cars would be included
in a simple random sample of three cars?
(a)
(b)
(c)
(d)
(e)
Plymouth, Lincoln, Chevy
Plymouth, Chevy, Porsche
Plymouth, Ford, Porsche
Lincoln, Plymouth, Porsche
Lincoln, Ford, Plymouth
_____17. Which of the following statements is true?
(a) A second sample of three beginning at a different position in the row would always produce the
same set of selections.
(b) A second sample of three beginning at a different position in the row would never include any of
the cars selected in question 16.
(c) Every subset of three cars would have the same chance of selection as the one identified in
question 16.
(d) The sample size is too large relative to the population size to conduct the sample.
(e) None of these statements is true.
_____18. The following students are available to serve on the Student Procrastination Committee.
1. Ally
7. Gina
13. Morris
2. Benji
8. Hank
14. Norm
3. Chad
9. Ivana
15. Olive
4. Donald
10. Jan
16. Patti
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5. Eli
11. Kyle
17. Quasimodo
6. Frannie
12. Lana
18. Ramone
Using the randInt function your TI-83, select a simple random sample size 4. Before you select your
sample, seed your random number generator by storing 7 into rand [ 7  rand ]. The students who were
selected were:
(a)
(b)
(c)
(d)
(e)
Ally, Ramone, Kyle, Olive
Donald, Ramone, Kyle, Frannie
Jan, Kyle, Kyle, Ramone
Gina, Ivana, Patti, Eli
Norm, Donald, Morris, Frannie
_____19. You have been given the task of determining if right-handed persons have stronger right
hands than left hands. A sample of 10 right-handed persons is selected randomly. Which of the
following designs would be most appropriate for this study?
(a) An observational study
(b) A design blocked for gender to determine if right-hand strength differs by gender
(c) A matched pair study in which each subject represents a block wherein the strength of the right
hand and the left hand is measured in random order
(d) Five of the subjects and randomly placed in the control group and the other in the treatment
group. All are tested and the results of each group are compared
(e) None of these is appropriate
_____20. Which of the following is an example of a census?
(a) Every fifth person leaving a supermarket is asked to name his or her favorite brand of peanut
butter.
(b) Each employee in a corporation fills out a questionnaire for a management survey.
(c) All the students who are at school on a particular day rate the food in the cafeteria.
(d) A telephone political poll selects ten names form every page of a city directory.
(e) All the commuters who are dissatisfied with the service of their commuter train company are
asked to write a letter of complaint.
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PART I Answers (2 points each)
1.
2.
3.
4.
5.
6.
7.
8.
9
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
PART II - Answer completely, but be concise. Write sequentially and show all steps. Show all your
work. Indicate clearly the methods you used, because you will be graded on the correctness of your
methods as well as on the accuracy of your results and explanations.
YOU MUST WRITE ANSWERS IN BY HAND – you need not print out the first 5 pages.
1. In competitive sports, video recorders have been used more frequently in recent years. The idea
behind the recorder is that coaches can replay training sessions for more effective feedback to the
athlete. Some people believe video recording may make the athletes more nervous and actually
decrease their performance. You have been asked to design an experiment to address this issue for
competitive high school tennis players. You have decided to use the accuracy of tennis serves as
your response variable, and the number of successful serves out of 100 as your performance
measure. The subjects for your experiment are 60 high school male competitive tennis players of
varying ability who have volunteered for the experiment.
a) Describe the treatments in your experiment. (4 points)
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b) One possible confounding variable is the experience levels of the players. Explain how you would
control this variable? (4 points)
2. 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 form 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). (12 points)
(a) List the treatments that the biologist that the biologist plans to use in this experiment.
(b) Using the treatments listed in part (a), describe a completely randomized design that will allow
the biologist to compare the shrimps’ growth after 3 weeks.
(c) Give one statistical advantage to having only tiger shrimps in the experiment. Explain why this
is an advantage.
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(d) Give one statistical disadvantage to having only tiger shrimps in the experiment. Explain why
this is a disadvantage.
3. One of the tasks of wildlife biologists is to estimate bird populations. One method for doing this is to walk a
“transect,” typically a long randomly selected rectangle, and count the number of particular species that are
seen. During hunting season the biologists wear brightly colored clothes as a protective measure. A theory,
known as the “species-confidence hypothesis,” predicts that birds may react to these brightly colored clothes.
A robin, for example, when confronted with a biologist wearing an orange color may be less afraid than if the
biologist were wearing a brown color. The idea is that the orange color gives the robin some “confidence”
that the biologist is another (really big!) bird. This is a difficulty because a robin that is less afraid of the
biologist may be easier to see and therefore “count” because the robin lets the biologist get closer. This
would result in too high an estimate of the robin population. To test this theory a biologist performed a study
in her area, wearing a bright orange vest or a brown vest while working. After training herself to accurately
estimate distances she indicated on her notes how close the robins would let her get before they flew away
(the “approach distance”), using this as a measure of their “confidence.” She randomly selected her starting
points in each trip through the transects and also carefully noted the weather conditions, specifically the wind
speed.
(a) What is the explanatory variable (factor) for this experiment? (4 points)
(b) What is the response variable for this experiment? (4 points)
(c) After completing the study the biologist was examining her results and noticed that on those days
she wore the brightly-colored vest the wind tended to be of greater velocity. How does this
information affect the interpretation of the results of the experiment? (4 points)
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4. The following paragraph describes an actual study. After reading the description, determine whether
the study is an observational study or an experiment. Justify your answer with specific references to
the information in the study. (6 points)
"We compared paired daytime and night counts of wild brook trout, brown trout, and rainbow
trout made by the same snorkelers in five streams during August 1994. Overall, we counted 109
trout in the daytime and 333 trout at night. We speculate that trout counted at night were present
during the daytime but were hidden from view. Biologists should consider that trout behavior
and susceptibility to being seen might vary a great deal between daytime and night, even during
summer. In some streams, the majority of trout may not be seen during the daytime."
5. When a tractor pulls a plow through an agricultural field, the energy needed 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 conducted 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 point. (12 points)
(a) What was the response variable in this study? Identify the treatments. What is the experimental
units?
(b) Given that the goal of the study is to determine whether a newly developed hitch reduced draft
compared to the standard hitch, was randomization used properly in this study? Justify your answer.
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(c) Given that the goal of the study is to determine whether a newly developed hitch reduced draft
compared to the standard hitch, was replication used properly in this study? Justify your answer.
(d) Plot of land is a confounding variable in this experiment. Explain why.
6. At the recently opened theme park, Six Samples Over a Population, a carnival game allows a player
three attempts, using a dart, to pop a balloon. As soon as the player pops the balloon, he wins the prize
and the game is over. If he does not pop the balloon after the third attempt he loses. Shenyan, an avid
dart-throwing balloon popper, estimates his probability of popping the balloon on the first attempt at
20%, popping the balloon on the second attempt at 30%, and popping the balloon on the third attempt at
40%. By describing an appropriate random digit assignment and performing 10 simulations using the
given random number table, determine the probability that Shenyan wins the prize. (10 points)
08424 44753 77377 28744 75592 08563 79140 92454
53645 66812 61421 47836 12609 15373 98481 14592
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