hello there is 9 multiple choice and 4 short answer the test is an hour and 30 minute long thank you
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MAT118 Spring 2017
Exam 3 Practice Solutions
Part I: Multiple Choice. Circle the best answer for each question.
1.
A two-way table is useful for describing which types of variables?
A.
B.
C.
D.
2.
two numerical variables
two categorical variables
one numerical variable
one numerical variable and one categorical variable
Is random sampling or random assignment the more important consideration if the research question
is whether members of one political party tend to donate more to charities than members of another
political party?
A. random sampling
3.
B. random assignment
A researcher is studying the relationship between a vitamin supplement and cholesterol level. What
type of study needs to be done to establish that the amount of vitamin supplement causes a change
in cholesterol level?
A. correlational study
B. randomized experiment
C. time series study
D. observational study
Questions 4–6 refer to the following situation: In a study published in Preventive Medicine (1991),
researchers Stampfer and Colditz observed that women who underwent hormone replacement therapy
(HRT) showed a lower risk of coronary heart disease (CHD).
4.
What are the observational units?
A. Whether underwent HRT
B. Risk of CHD
5.
Which of the following is the explanatory variable?
A. Whether underwent HRT
B. Risk of CHD
6.
C. Women
D. Does HRT lower risk of CHD?
C. Women
D. Does HRT lower risk of CHD?
Which of the following is the response variable?
A. Whether underwent HRT
B. Risk of CHD

C. Women
D. Does HRT lower risk of CHD?
Exam 3 Practice Solutions, page 1 of 13
7.
In a recent school poll, the administrators asked if students were satisfied with the school’s course
offerings. What is the population of interest?
A.
B.
C.
D.
8.
A gym is offering a new 6-week weight loss exercise program for its members. Members who sign
up for the program are weighed and measured once a week for the duration of the program. The
owners of the gym want to know if the weight loss program actually helps people lose weight.
What variable could be a possible confounding factor in determining the cause of weight loss?
A.
B.
C.
D.
9.
All students who are satisfied with the course offerings
All students who are not satisfied with the course offerings
All students who attend the school
All students who participated in the poll
The person’s commitment to the program
The person’s marital status
The person’s family structure
The person’s diet
A team in the Department of Institutional Review at a large university wanted to study the
relationship between completing an internship during college and students’ future earning potential.
From the same graduating class, they selected a random sample of 80 students who completed an
internship and 100 students who did not complete an internship and examined their salaries 5 years
past graduation. They found that there was a statistically higher mean salary for the internship
group than for the no internship group. Which of the following interpretations do you think is the
most appropriate?
A. More students should take internships because having an internship produces a higher salary.
B. There could be a confounding variable, such as student major, that explains the difference
in mean salary between the internship and no internship groups.
C. You cannot draw any valid conclusions because the samples are not the same size.
10. What does it mean for an experiment to be double-blind?
A. The researcher does not know which participants are in the treatment and control groups.
B. The participants do not know who is in the treatment and control groups.
C. Neither the researcher nor the participants know who is in the treatment and control
groups.
D. The researcher and the participants know which group they are in because it is unethical to keep
this information from them.
Exam 3 Practice Solutions, page 2 of 13
Questions 11 and 12 refer to the following situation: The engineering department of Westvaco’s
envelope division went through a workforce reduction. The table below shows the number of workers
who were laid off and retained, classified by age.
Under 50
50 or older
Total
Laid off
6
12
18
Retained
10
8
18
Total
16
20
36
11. Does there appear to be age discrimination in the workforce reduction decisions?
A. No, since the same number of employees (18) were laid off as retained.
B. Yes, since 66.7% (12/18) of workers 50 and older compared to 33.3% (6/18) of workers under
50 were laid off.
C. Yes, since 60.0% (12/20) of workers 50 and older compared to 37.5% (6/16) of workers
under 50 were laid off.
D. No, since we cannot determine association without random assignment.
12. Why are percentages more useful than counts to determine whether there was age discrimination?
A.
B.
C.
D.
There are more workers under 50 than 50 and older in the sample.
The same number of employees were laid off as retained.
You should only use counts in a two-way table.
You should only use percentages in a two-way table.
13. A Canadian study examined whether giving antibiotics in infancy increases the likelihood that the
child will be overweight later in life. The children were classified as having received antibiotics or
not during the first year of life and then being overweight or not at 9 years old. If a segmented bar
graph is created to display the study data, which of the following would be the most appropriate
labels on the horizontal axis?
A. Overweight and Not overweight
B. Antibiotics and No antibiotics
Questions 14–16 refer to the following situation: The Physicians’ Health Study is a very large,
randomized study designed to “test the effects of low-dose aspirin…in the prevention of cardiovascular
disease (CVD).” The subjects were 22,071 U.S. male physicians (aged 40–84 years, in the year 1982)
who were randomly assigned to be in either the low-dose aspirin group or the placebo group. Each
participant was required to take the assigned pill every other day for five years. The study was double
blind. Of the 11,034 physicians who took the placebo, 189 suffered heart attacks during the study. Of
the 11,037 physicians who took aspirin, 104 had heart attacks.
Exam 3 Practice Solutions, page 3 of 13
14. Which of the following is the appropriate null hypothesis for this study?
A. The probability of a heart attack for those taking aspirin is the same as for those taking
the placebo.
B. The probability of a heart attack for those taking aspirin is smaller than for those taking the
placebo.
C. The probability of a heart attack for those taking aspirin is greater than for those taking the
placebo.
D. The probability of a heart attack for those taking aspirin is different than for those taking the
placebo.
15. Which of the following is the appropriate alternative hypothesis for this study?
A. The probability of a heart attack for those taking aspirin is the same as for those taking the
placebo.
B. The probability of a heart attack for those taking aspirin is smaller than for those taking the
placebo.
C. The probability of a heart attack for those taking aspirin is greater than for those taking the
placebo.
D. The probability of a heart attack for those taking aspirin is different than for those taking
the placebo.
16. A simulation analysis was performed using the sample data, and the resulting p-value was 0/1000.
Which of the following is the correct interpretation of this p-value?
A. The results are statistically significant. We have very strong evidence that the probability
of a heart attack for those taking aspirin is different than for those taking the placebo.
B. The results are not statistically significant. We have little to no evidence that the probability of
a heart attack for those taking aspirin is different than for those taking the placebo.
C. The results are not statistically significant. It is plausible that the probability of a heart attack
for those taking aspirin is not the same as for those taking the placebo.
D. The results are statistically significant. We have little to no evidence that the probability of a
heart attack for those taking aspirin is smaller than for those taking the placebo.
Exam 3 Practice Solutions, page 4 of 13
Questions 17 and 18 refer to the following situation: Suppose that three high school students
separately conduct polls in their city to investigate if there is an association between being a vegetarian
and whether people like to eat at home or eat at restaurants.
•
•
•
Sally finds that 35 out of 45 vegetarians preferred to eat at restaurants whereas 20 out of 105
nonvegetarians preferred to eat at home.
Tara finds that 70 out of 90 vegetarians preferred to eat at restaurants whereas 40 out of 210
nonvegetarians preferred to eat at home.
Uma finds that 30 out of 45 vegetarians preferred to eat at restaurants whereas 25 out of 105
nonvegetarians preferred to eat at home.
17. Comparing Sally’s study to Tara’s study: Who will find stronger evidence of a difference between
vegetarians and nonvegetarians with regard to preference to eat at home? Answer without using
any applets.
A.
B.
C.
D.
Sally
Tara
The strength of evidence will be similar.
Cannot be answered without finding a p-value
18. Comparing Sally’s study to Uma’s study: Who will find stronger evidence of a difference between
vegetarians and nonvegetarians with regard to preference to eat at home? Answer without using
any applets.
A.
B.
C.
D.
Sally
Uma
The strength of evidence will be similar.
Cannot be answered without finding a p-value
19. A Pew Research study in April and May of 2013 asked single American adults whether they have
ever broken up with someone by email, text, or online message. They found that 18.0% (52/289) of
women and 15.1% (55/364) of men said they had broken up with someone by email, text, or online
message. Which of the following is the correct calculation and interpretation of the relative risk
(RR) in this case?
A. RR = 0.151/0.180 = 0.833: Men in the sample were 83.3% more likely than women to have
broken up with someone by email, text, or online message.
B. RR = 0.151/0.180 = 0.833: Men in the sample were 0.833 times more likely than women to
have broken up with someone by email, text, or online message.
C. RR = 0.180/0.151 = 1.192: Women in the sample were 1.192% more likely than men to have
broken up with someone by email, text, or online message
D. RR = 0.180/0.151 = 1.192: Women in the sample were 1.192 times more likely than men to
have broken up with someone by email, text, or online message.
Exam 3 Practice Solutions, page 5 of 13
20. An instructor is going to model an experiment in his statistics class by comparing the effect of 4
different treatments on student response. There are 40 students in the class. Which of the following
is the best way for the instructor to distribute the students to the 4 treatments for this experiment?
A. Assign the first treatment to the first 10 students on the class list, the second treatment to the
next 10 students, and so on.
B. Assign a unique number to each student, then use random numbers to assign 10 students
to the first treatment, 10 students to the second treatment, and so on.
C. Assign the treatment as students walk into class, giving the first treatment to the first 10
students, the second treatment to the next 10 students, and so on.
D. All of these are equally appropriate methods.
E. None of these is an appropriate method.
21. A 2013 Gallup poll asked randomly selected U.S. adults whether they wanted to stay at their current
body weight or change. One purpose was to investigate whether there was any difference between
men and women with respect to this question. The sample proportion of men who wanted to stay at
their current weight was p^M = 242/562 = 0.431 and the sample proportion of women who wanted to
stay at their current weight was p^F = 172/477 = 0.361. A 95% confidence interval for the difference
in population proportions was found to be (0.011, 0.130). Which of the following is the correct
interpretation of the confidence interval?
A. We are 95% confident that the population proportion of men who want to stay at their
current weight is between 0.011 and 0.130 higher than the population proportion of
women who want to stay at their current weight.
B. We are 95% confident that the population proportion of women who want to stay at their current
weight is between 0.011 and 0.130 higher than the population proportion of men who want to
stay at their current weight.
C. We are 95% confident that the population proportion of women who want to stay at their current
weight is between 1.1% and 13.0%.
D. There is a 95% chance that the population proportion of men who want to stay at their current
weight is between 1.1% and 13.0%.
Questions 22–25 refer to the following situation: A team of researchers (Singer et al., 2000) used the
Survey of Consumer Attitudes to investigate whether incentives would improve the response rates on
telephone surveys. A national sample of 735 households was randomly selected, and all 735 of the
households were sent an “advance letter” explaining that the household would be contacted shortly for a
telephone survey. However, 368 households were randomly assigned to receive a monetary incentive
along with the advance letter, and of these 286 responded to the telephone survey. The other 367
households were assigned to receive only the advance letter, and of these 245 responded to the telephone
survey. Suppose we want to use cards to conduct a tactile simulation to generate a p-value to test the
hypothesis that monetary incentives improve response rates on telephone surveys.
Exam 2, page 6 of 13
22. How many cards would be needed for the simulation?
A. 367
B. 368
C. 286
D. 245
E. 735
23. Suppose we are using red and black cards. How many of each color would we need and what
would each color represent?
A. We would need 286 red cards to represent the households that received a monetary incentive
and responded to the survey and 245 black cards to represent the households that did not receive
a monetary incentive and responded to the survey.
B. We would need 286 red cards to represent the households that received a monetary incentive
and responded to the survey and 82 black cards to represent the households that received a
monetary incentive and did not respond to the survey.
C. We would need 245 red cards to represent the households that did not receive a monetary
incentive and responded to the survey and 122 black cards to represent the households that did
not receive a monetary incentive and did not respond to the survey.
D. We would need 531 red cards to represent the households that responded to the survey
and 204 black cards to represent the households that did not respond to the survey.
24. We will shuffle the cards and deal them into multiple piles. How many piles should we make and
how many cards should we place in each pile?
A.
B.
C.
D.
We should deal 368 cards to one pile and 367 cards to a second pile.
We should deal 286 cards to one pile and 245 cards to a second pile.
We should deal all the cards into one pile.
We should deal 531 cards to one pile and 204 cards to a second pile.
25. Suppose that after each shuffle and deal, we record the difference in proportion of red cards
between the two piles. We do this 1000 times, so we have recorded 1000 differences. What should
we do to find the p-value for this simulation?
A.
B.
C.
D.
Determine what proportion of the 1000 differences are greater than or equal to 0.777.
Determine what proportion of the 1000 differences are greater than or equal to 0.110.
Determine what proportion of the 1000 differences are less than or equal to 0.668.
Determine what proportion of the 1000 differences are greater than or equal to 0.777 or less than
or equal to 0.668.
Exam 3 Practice Solutions, page 7 of 13
Part II: Short Answer. Note that on the exam you will need to show your work and/or explain how
you arrived at your answer in order to receive full credit
1. Psychologists investigated whether praising a child’s intelligence, rather than praising his/her effort,
tends to have negative consequences such as undermining their motivation (Mueller and Dweck,
1998). Children participating in the study were given a set of problems to solve. After the first set
of problems, half of the children were randomly assigned to be praised for their intelligence, while
the other half was praised for their effort. The children were then given another set of problems to
solve and later told how many they got right. They were then asked to write a report about the
problems for other children to read, including information about how many they got right. Of the 29
children who were praised for their intelligence, 11 misrepresented (i.e., lied about) how many they
got right. Of the 30 children who were praised for their effort, 4 misrepresented how many they got
right. Researchers were interested in learning whether there was a difference in the proportion of
children who lied depending on how they were praised.
a. Was this an observational study or an experiment? Explain how you know. Identify the
observational/experimental units.
Since the children were randomly assigned to receive either praise for
intelligence or praise for effort, this is an experiment. The experimental units are
the children.
b. Identify the explanatory and response variables in this study.
The explanatory variable is whether the child was praised for intelligence or
praised for effort.
The response variable is whether the child lied about how many problems they
got right.
c. Fill in the table below based on the description of the study results, including the row and
column labels.
Praised for
intelligence
Praised for
effort
Total
Lied
11
4
15
Did not lie
18
26
44
Total
29
30
59
Exam 3 Practice Solutions, page 8 of 13
d. For each treatment group, determine the proportion who lied and use an appropriate symbol for
each proportion.
^ I = 11/29 = 0.379 = 37.9% lied
Praised for intelligence: p
^ E = 4/30 = 0.133 = 13.3% lied
Praised for effort: p
e. State the null and alternative hypotheses for this study in words and symbols.
H0: The (population) proportion of all children who lie about how many problems
they get correct is the same whether they are praised for their intelligence or
their effort. There is no association between the type of praise and whether a
child lies.
H0: pI – pE = 0
Ha: The (population) proportion of all children who lie about how many problems
they get correct is different for children who are praised for their intelligence
compared to children who are praised for their effort. There is an association
between the type of praise and whether a child lies.
Ha: pI – pE ? 0
f. Use an appropriate applet to conduct a simulation with 1000 repetitions. State which applet you
used, what you entered into the applet, and report the p-value.
We use the Two Proportions applet as shown below. The counts from the twoway table are entered into the 2 x 2 table in the applet. The observed
^I – p
^ E = 0.379 – 0.133 = 0.246, which is entered into
difference in proportions is p
the Count box to find the p-value. We choose “Beyond” since we are
conducting a two-sided test (the alternative hypothesis has a ? symbol). The
p-value is 46/1000 = 0.046.
Exam 3 Practice Solutions, page 9 of 13
Exam 3 Practice Solutions, page 10 of 13
g. Interpret the p-value in the context of the study.
We have strong evidence that the proportion of all children who lie about how
many problems they get correct is different for children who are praised for
their intelligence compared to children who are praised for their effort. If the
proportion of all children who lie about how many problems they get correct is
the same whether they are praised for their intelligence or their effort, then
there is a 4.6% chance that we would see a …
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