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 46 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 schools 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 persons commitment to the program

The persons marital status

The persons family structure

The persons 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 Westvacos

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 1416 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 4084 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 Sallys study to Taras 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 Sallys study to Umas 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 2225 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 childs 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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