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Name ________________________
AP Statistics
Date _____________
Schwimmer
Midterm Review #2
1.
Jason wants to determine how age and gender are related to political party preference in
his town. Voter registration lists are stratified by gender and age-group. Jason selects a
simple random sample of 50 men from the 20-29 age-group and records their age, gender,
and party registration (Democratic, Republican, neither). He also selects an independent
simple random sample of 60 women from the 40-49 age-group and records the same
information. Of the following, which is the most important observation about Jason’s
plan?
(1)
(2)
(3)
(4)
The plan is well conceived and should serve the intended purpose.
His samples are too small.
He should have used equal sample sizes.
He should have randomly selected the two age groups instead of choosing them
nonrandomly.
(5) He will be unable to tell whether a difference in party affiliation is related to
differences in age or to the difference in gender.
2.
A study of existing records of 27,000 automobile accidents involving children in
Michigan found that about 10 percent of children who were wearing a seatbelt (group
SB) were injured and that about 15 percent of children who were not wearing a seatbelt
(group NSB) were injured. Which of the following statements should not be included in
a summary report about this study?
(1)
(2)
(3)
(4)
(5)
3.
Driver behavior may be a potential confounding factor.
The child’s location in the car may be a potential confounding factor.
This study was not an experiment, and cause-and-effect inferences are not warranted.
This study demonstrates clearly that seat belts save children from injury.
Concluding that seat belts save children from injury is risky, at least until the study is
independently replicated.
Which of the following statements is true for two events, each with probability greater
than 0?
(1)
(2)
(3)
(4)
(5)
If the events are mutually exclusive, they must be independent.
If the events are independent, they must be mutually exclusive.
If the events are not mutually exclusive, they must be independent.
If the events are not independent, they must be mutually exclusive.
If the events are mutually exclusive, they cannot be independent.
4.
A fair coin is to be flipped 5 times. The first 4 flips land “heads” up. What is the
probability of “heads” on the next (5th) flip of this coin?
(1) 1
1
(2)
2
4
 5  1   1 
(3)      
1 2   2 
4
1 1
(4)    
2 2
(5) 0
5.
Which of the following is NOT a characteristic of stratified random sampling?
(1)
(2)
(3)
(4)
(5)
6.
Random sampling is part of the sampling procedure.
The population is divided into groups of units that are similar on some characteristic.
The strata are based on facts known before the sample is selected.
Each individual unit in the population belongs to one and only one of the strata.
Every possible subset of the population, of the desired sample size, has an equal
chance of being selected.
a. A new medication has been developed to treat sleep-onset insomnia (difficulty in
falling asleep). Researchers want to compare this drug to a drug that has been used in the
past by comparing the length of time it takes subjects to fall asleep. Of the following,
which is the best method for obtaining this information?
(1) Have subjects choose which drug they are willing to use, then compare the results.
(2) Assign the two drugs to the subjects on the basis of their past sleep history without
randomization, then compare the results.
(3) Give the new drug to all subjects on the first night. Give the old drug to all subjects
on the second night. Compare the results.
(4) Randomly assign the subjects to two groups, giving the new drug to one group and no
drug to the other group, then compare the results.
(5) Randomly assign the subjects to two groups, giving the new drug to one group and
the old drug to the other group, then compare the results.
b. Can you think of a better way to complete a study to obtain the same information as
above?
Matched pairs pairing each subject with himself. Randomly assign subjects into two
groups. Group 1 uses treatment 1 the first night and treatment 2 a week later. Group 2
uses treatment 2 the first night and treatment 1 a week later. Then, compare the results
for each patient.
7.
A spinner on a full circle can take on any decimal value between 0 and 400. What is the
probability that the spinner will land between 175 and 225?
(1)
(2)
(3)
(4)
(5)
8.
50
400
56
400
175
400
200
400
225
400
0
300
100
200
Records from a random sample of dairy farms for the years 1998-2003 yielded the
information below on the number of male and female calves born at various times of the
day.
Males
Females
Total
Day
129
118
247
Evening
15
18
33
Night
117
116
233
Total
261
252
513
What is the probability that a randomly selected calf was born in the night or was a
female?
(1)
(2)
(3)
(4)
(5)
9.
369
513
485
513
116
513
116
252
116
233
A fast-food establishment has many different products for sale. Suppose that 60% of all
customers order a hamburger of some kind, 12% purchase a milkshake, and 5% order
both. If a customer is randomly selected, what is the probability that he or she ordered
neither a hamburger nor a milkshake?
(1) 0.05
(2) 0.28
(3) 0.33
(4) 0.48
(5) 0.60
H
M
.55 .05 .07
.33
10.
A suburban school has 4 classes: freshmen, sophomores, juniors, and seniors. The
administration wants to compare the quality and taste of the current company that
provides pizza at lunch (A) with another company (B). It is interested in which pizza the
students like the most, A or B. The population of the school is 1,000 students with each
class having roughly the same number of students. A stratified random sample of 40
students will be chosen to taste the pizza (plain pizza only) with each class having equal
representation.
(a) Decide exactly how you will label the students in order to select your sample. Since
you are going to be using a table of random numbers, think this through first.
Obtain an alphabetical list of students. Label the students 000-999. Each subject in
the experiment will be represented by 3 digits in a table of random digits. Pull off
strings of 3-digit numbers until you have 40 people in your sample (ignore repeats
since each 3-digit number represents a person). Since our sample is stratified, you
should stop when you get 10 people per class. For example, disregard additional
freshmen chosen once you get 10 freshmen.
(b) Use Table B, beginning at line 130, to select the first 6 students in the sample.
(This can be done in different ways!)
690, 516, 481, 787, 174, 095
(c) Diagram how the following experiment would be set up.
i) completely randomized
Group 1
Treatment 1
20 students
Random
40 students
Assignment
Group 2
Treatment 2
20 students
Compare preference
in pizza
Treatment 1: Eat pizza from company A and decide if they like it.
Treatment 2: Eat pizza from company B and decide if they like it.
ii) block design with 2 blocks (lower grades 9 and 10 vs. upper grades 11 and 12)
Group 1
10 students
Block 1
Random
Lower grades
Assignment
Block 2
Random
Upper grades
Assignment
40 students
Group 2
10 students
Group 3
10 students
Group 4
10 students
Treatment 1
Compare
preference
Treatment 2
Treatment 1
Compare
preference
Treatment 2
Treatment 1: Eat pizza from company A and decide if they like it.
Treatment 2: Eat pizza from company B and decide if they like it.
iii) matched pairs (students acting as their own control)
Group 1
Treatment 1
20 students
40 students
Random
Compare preference
Assignment
in pizza
Group 2
20 students
Treatment 2
Treatment 1: Eat pizza from company A on first day, then eat pizza from
company B on second day.
Treatment 2: Eat pizza from company B on first day, then eat pizza from
company A on second day.
(d) A decision is made to go with the matched pairs design. Assuming that the
experimenters have taken reasonable precautions, describe a lurking variable that
could present itself in trying to identify what pizza (A or B) the students prefer.
Students may recognize the current company’s pizza (A) and because they are
accustomed to eating it, they may confuse that recognition with a preference.
(This is not the only possible solution!!)