STAT 110 Practice Questions for Exam 1 – Fall 2012
True/False Questions: Circle the correct answer.
1. The binomial distribution is a commonly used distribution in statistics because there are no
assumptions to worry about. (TRUE or FALSE)
2.
A dermatologist records whether or not a patient has any moles greater than ¼ inch in diameter.
This is an example of a categorical variable. (TRUE or FALSE)
3.
The same dermatologist records the actual diameter of any mole greater than ¼ inch. This is an
example of a categorical variable. (TRUE or FALSE)
4.
Statistical inference involves making claims about populations based on data obtained from samples.
(TRUE or FALSE)
In a standard test for ESP (extrasensory perception), the experimenter looks at cards that are hidden
from the subject. Each card contains either a star, a circle, a wave, or a square. As the experimenter
looks at each of the 20 cards in turn, the subject names the shape on the card. The hypotheses are as
follows:
Ho: The subject is just guessing.
Ha: The subject has ESP.
5.
Suppose a subject correctly identifies the shape on 10 of the 20 cards, resulting in a p-value of .0139.
This p-value can be interpreted as follows: If the subject is just guessing, there is only a 1.39% chance
of getting results at least as extreme as the 10 correct identifications. (TRUE or FALSE)
6.
Consider the previous problem. The p-value of .0139 can be interpreted as follows: There is only a
1.39% chance the subject is guessing. (TRUE or FALSE)
7.
Once again, consider problem 5. Given that the p-value is .0139, we have statistical evidence that the
subject is getting more correct than we expect by guessing, so they may have ESP. (TRUE or FALSE)
Multiple Choice Questions:
8. An insurance company states that 90% of its claims are settled within 30 days. A consumer group
believes that the true proportion is actually less than 90%, so they select a random sample of 20 of the
company’s claims to test this statement. The following hypotheses are examined:
Ho: The insurance company’s claim is true (90% of claims are settled within 30 days).
Ha: The true proportion of claims settled within 30 days is less than 90%.
Suppose a binomial test is carried out, and the p-value for this problem is .0432. Which of the following is
the most correctly written conclusion?
a. The sample size is too small to draw a valid conclusion.
b. We have evidence that the proportion of claims settled within 30 days is less than 90%.
c. We have evidence that the proportion of claims settled within 30 days is NOT less than 90%.
d. Without a doubt, the proportion of claims settled within 30 days is less than 90%.
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9. A graduate student is designing a research study. She is hoping to show that the results of an
experiment are statistically significant. What type of p-value would she want to obtain?
a. A large p-value.
b. A small p-value.
c. The magnitude of a p-value has no impact on statistical significance.
10. Assume a study is carried out and the researchers obtain a p-value of .4144. Which of the following is
the most correctly written conclusion?
a. This p-value gives strong evidence in support of the alternative hypothesis (i.e., the research question)
because it is small.
b. This p-value gives strong evidence in support of the alternative hypothesis (i.e., the research question)
because it is large.
c. This p-value does not give evidence in support of the alternative hypothesis (i.e., the research question)
because it is small.
d. This p-value does not give evidence in support of the alternative hypothesis (i.e., the research question)
because it is large.
11. Again, consider the study in which researchers obtained a p-value of .4144. Which of the following is
the most correct interpretation of this p-value?
a. There is a 41.44% chance the null hypothesis is true.
b. If the null hypothesis is true, there is a 41.44% chance of observing data at least as extreme as the
results seen in the study.
c. If the alternative hypothesis is true, there is a 41.44% chance of observing data at least as extreme as the
results seen in the study.
d. There is a 41.44% chance the alternative hypothesis is true.
12. Which of the following statements best describes the relationship between a parameter and a statistic?
a. A parameter varies according to a sampling distribution which is centered at the value of the statistic.
b. A parameter is used to estimate a statistic.
c. A statistic is used to estimate a parameter.
d. There is no relationship between a parameter and a statistic.
13. Male swordtail fish exhibit a pattern of dark vertical bars on their sides that become darker when
courting a female. An experiment was carried out in which a female fish was placed in a tank with both a
symmetric male (which has the same number of bars on each side of the fish) and a non-symmetric male
(which has a different number of bars on each side). The same experiment was repeated with two other
females, so there were a total of three trials. The researchers recorded whether or not the female fish
preferred to associate with the symmetric male, and out of the three females in the study, all three
preferred the symmetrical male.
The null and alternative hypotheses are given as follows:
Ho: females have no preference
Ha: females prefer the males with a symmetric pattern.
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A binomial exact test was used to analyze the data, giving a p-value of .125. Which of the following is the
most correctly written conclusion?
a. Using a significance level of .05, we have evidence that females prefer males with a symmetric pattern
because all three females in the study chose the symmetric male.
b. Using a significance level of .05, we have evidence that females prefer males with a symmetric pattern
because the p-value is above .05.
c. Using a significance level of .05, we do NOT have evidence that females prefer males with a symmetric
pattern because the p-value is above .05.
d. The sample size is too small to use the binomial exact test.
14. A standard test for extrasensory perception (ESP) asks subjects to identify which of four shapes (circle,
square, triangle, or diamond) is on the front of a card, viewed by the experimenter but not the subject.
Suppose that a subject takes a test with 40 of these cards and gets 12 correct. Based on the binomial
distribution, the probability of getting 12 or more correct by guessing is 28.5%. Which of the following is
the most correct conclusion?
a. We have no evidence that the subject has ESP because there is a large probability (28.5%) of observing
results such as these even if the subject is guessing.
b. We do have evidence that the subject has ESP because there is a large probability (28.5%) of observing
results such as these even if the subject is guessing.
c. We have no evidence that the subject has ESP because the probability of getting 12 or more correct by
guessing (28.5%) is close to the probability of getting one trial correct by guessing (1/4=25%).
d. We do have evidence that the subject has ESP because the probability of getting 12 or more correct by
guessing (28.5%) is close to the probability of getting one trial correct by guessing (1/4=25%).
15. A student participates in a Coke versus Pepsi taste test. She correctly identifies which soda is which
four times out of six tries. She claims that this proves that she can reliably tell the difference between the
two soft drinks. You have studied statistics and you want to determine the probability of anyone getting
at least four right out of six tries just by guessing. Which of the following would provide an accurate
estimate of that probability?
a. Have the student repeat this experiment many times and calculate the percentage of times she correctly
distinguishes between the brands.
b. Simulate this 1,000 times on the computer with a 50% chance of guessing the correct soft drink on each
try, and calculate the percent of times there are four or more correct guesses out of six trials.
c. Repeat this experiment with a very large sample of people and calculate the percentage of people who
make four correct guesses out of six tries.
d. All of the methods listed above would provide an accurate estimate of the probability.
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16. In 2009, an Associated Press/mtvU poll surveyed undergraduate students (ages 18 to 24) at four-year
colleges in the U.S., exploring the students' state of mind and the pressures they face. The poll was
conducted April 22 to May 4, 2009, by Edison Media Research and involved interviews with 2,240
randomly selected students. Of those surveyed, 941 reported that they had felt down, depressed or
hopeless several days during the past two weeks.
a. Identify the population of interest.
b. Identify the sample in this study.
c. Identify the sample statistic.
17. On February 1-3 of 2010, 1,072 adults nationwide were randomly sampled and asked the following
question: “A pro-life, pro-family commercial sponsored by the advocacy group Focus on the Family will air during
the Super Bowl. It features a Heisman Trophy winner, Florida Gators quarterback Tim Tebow, and his mother. Do
you agree or disagree with the decision by CBS to air this commercial during the Super Bowl?” Source:
http://pollingreport.com/football.htm.
a. Consider the following statement: “Out of 1,072 respondents, 643 (60%) said that they did agree.” Is
this an example of INFERENTIAL or DESCRIPTIVE statistics? (circle one)
b. Consider the following statement: “A hypothesis test was carried out, and it was found that these data
do provide evidence that the majority of adults nationwide agree with the decision by CBS to air this
commercial.” Is this an example of INFERENTIAL or DESCRIPTIVE statistics? (circle one)
18. Consider the previous problem. Once again, 60% of the 1,072 survey respondents did agree with the
CBS decision to air the commercial. Researchers wanted to use these results to provide evidence that the
majority of all adults nationwide agreed with CBS. So, a statistician helped carry out the hypothesis test
and summarized the results as follows: “If only half of adults nationwide agreed with the decision to air
the commercial, the probability of observing 60% or more respondents who agree in this survey is
.0000000000336. Because this probability is less than .05, we can conclude that the majority of adults
nationwide agree with the decision.”
a. Fill in the blanks to indicate which of the following statements is the NULL (H o) and which is the
ALTERNATIVE (Ha) hypothesis.
__________: The proportion of adults nationwide who feel the commercial should air is equal to 50%.
__________: The proportion of adults nationwide who feel the commercial should air is greater than 50%.
b. Based on the information from above, give a numerical value for each of the following. Note that there
is no need to calculate anything – all of the information you need has been given.
i. The p-value. _____________
ii. The sample proportion. _____________
iii. The sample size. ______________
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19. Social workers deal with traumatic stories on a regular basis (e.g. working with victims of sexual
assault, victims of Hurricane Katrina, etc.) and some recent research has indicated that repeatedly hearing
the stories of trauma victims increases the risk of social workers themselves experiencing post-traumatic
stress disorder (PTSD). It is known that 7.8% of the general population experiences PTSD in a lifetime.
Suppose that a survey of 39 social workers found that 6 suffered from PTSD.
a. Recall that there are 39 social workers in this study. Use the CORRECT Excel output to find the
probability of 7 or more experiencing PTSD, assuming that social workers experience PTSD at the same
rate as does the general population.
OUTPUT # 1
Binomial with n = 39 and p = 7.8%
OUTPUT # 2
Binomial with n = 39 and p = 15.4%
b. Based on the probability from part (a) can we conclude that the rate of PTSD is greater for
social workers than it is for the general population? Explain your answer.
20. A study was conducted to determine whether Winona State students were more likely to identify
themselves as liberals versus conservatives. Suppose that 97 students were randomly selected and
surveyed, and 55 identified themselves as liberals.
The dot plot below shows the results of a simulation study carried out using coin flips to investigate
this question. A coin landing heads up represents a student that identifies themselves as liberal; a
coin landing tails up represents a student that identifies themselves as conservative. Note that this
simulates the situation where the population of all WSU students consists of half liberals, and half
conservatives. This experiment was repeated 100 times, and each time the number of heads out of 97
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tosses (i.e, the number of liberals in the sample) was collected and recorded in the following dotplot.
a.
How many coin flips will we need for this simulation study? Circle the correct answer. (3
pts)
i.
ii.
iii.
iv.
About 8500 -- One for each WSU student in the population.
97 -- One for each student in the sample.
55 – One for each student in the sample who said they were liberal.
100 – One for each simulated result.
b. What does each dot on the dotplot represent? Circle the correct answer. (3 pts)
i. A student that identified themselves as liberal.
ii. The number of students (out of 100) identifying themselves as liberal, assuming
the population of all WSU students consists of half liberals and half
conservatives.
iii. The number of students (out of 97) identifying themselves as liberal, assuming
the population of all WSU students consists of half liberals and half
conservatives.
iv. The number of students (out of 97) identifying themselves as liberal, assuming
the majority of all WSU students are liberal.
c.
Recall that 55 out of 97 students in the sample identified themselves as liberals. Based on
the above simulation, do you think this experiment provides evidence that the majority of
all WSU students identify themselves as liberal? Explain. (5 pts)
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21. In a sample of n= 300 WSU students with declared majors the following results were
obtained when considering the college their declared major is in and whether or not they
reported skipping at least one class per week.
a.) What is the data type of both of these variables?
b.) Students which in college had the highest percentage skipping at least one class per
week? What was this percentage?
c.) What percentage of students reported not skipping any classes per week in the College
of Education?
d.) What do we estimate is the percentage of WSU students with declared majors who skip
at least one class per week?
e.) What do we estimate is the percentage of WSU students whose declared major is in the
College of Liberal Arts? College of Science and Engineering?
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22. In a sample of n = 254 WSU students who send text messages, the following results were
obtained regarding the number of text messages they sent per day.
a) Which statistic should be used to summarize the typical number of texts sent by WSU
students and why?
b) What is the “typical” number of texts sent per day by WSU students who send text
messages?
c) How would you characterize the distributional shape?
d) What is the coefficient of variation?
23. In a sample of n = 254 WSU students who send text messages there were 166 females and 88
makes. The plot and summary statistics below show a comparison of the number of text
messages sent by these students across gender.
a)
Compare and contrast the number of text messages sent by female and male WSU
students who text?
b) 75% of WSU females send more than ______ text messages per day?
c) 90% of WSU males send fewer than _______ text messages per day?
d) True or False – the mean for females is greater than that for males because there were
more females sampled.
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e)
True or False – the coefficient of variation of the number of texts sent per day is greater
than 100% for both males and females.
f) True or False – the interquartile range (IQR) for the number texts sent per day by males
is greater than that for females?
24. On March 17, 2010, the results of a Gallup survey indicated that 16.3% of American adults surveyed
were without health coverage in January and February of this year. Gallup also reported that “one can
say with 95% confidence that the maximum margin of error is ±1 percentage point.”
a. Find an approximate 95% confidence interval for the proportion of all American adults who were
without health coverage in January and February of this year. You can assume the margin of error is ±1%.
b. If all other quantities were unchanged, an increase in the sample size will lead to a wider interval.
(True or False)
c. The population proportion (i.e., the proportion of all American adults who were without health
coverage in January and February of this year) will definitely be contained in this confidence interval.
(True or False)
d. The sample proportion (𝑝̂ ) will definitely be contained in this confidence interval. (True or False).
e. If we increased the confidence level to 99% the confidence interval would be narrower (True or False).
25. Another Gallup survey asked respondents that were insured about the source of their coverage. A
95% confidence interval was calculated for the proportion of all American adults that have relied on
government coverage (Medicare, Medicaid, or military/veteran’s benefits) so far in 2010. This confidence
interval is given by (23.6%, 25.6%).
a. This confidence interval means that we are 95% certain the proportion of American adults that have
relied on government health coverage so far this year falls between 23.6% and 25.6%. (True or False)
b. This confidence interval means that we are 95% certain the difference between the proportion of
American adults that have relied on government health coverage so far this year and the proportion that
have not falls between 23.6% and 25.6%. (True or False)
26. In the WSU student survey we conducted this semester we found that 120 of the 332 students
sampled reported having blue eyes. Find and interpret a 95% confidence interval for the proportion of
WSU students in the population that have blue eyes.
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True/False Questions: Circle the correct answer.
Questions 1-4 concern the following scenario. Suppose that 1,000 Minnesotans are randomly selected and
asked about both their political affiliation and whether they support the Voter ID law.
1.
2.
3.
4.
5.
6.
7.
Fisher’s exact test can be used to obtain a single p-value to compare the proportion that
supports the law between democrats and republicans.
TRUE
FALSE
A chi-square test can be used to obtain a single p-value to compare the proportion that
supports the law between democrats and republicans.
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
TRUE
FALSE
Fisher’s exact test can be used to obtain a single p-value to compare the proportion that
supports the law between democrats, independents, and republicans.
A chi-square test can be used to obtain a single p-value to compare the proportion that
supports the law between democrats, independents, and republicans.
A study is designed to test for a relationship between a dog’s breed and the occurrence of
Lyme’s disease. If a small p-value (say less than .01) is obtained from a Chi-square test,
this means that there is no relationship between these two variables.
While observational studies may suggest relationships, great care must be taken in
concluding that there is cause and effect because of the lack of control over lurking
variables.
When finding expected counts to be used in the calculation of a chi-square test statistic,
we assume that the alternative hypothesis (not the null) is true.
8.
A mosaic plot is a graphical representation of counts from a contingency table.
TRUE
FALSE
9.
In general, if a relative risk is equal to 1, this means there is a significant difference in the
outcome of interest between the two groups.
TRUE
FALSE
Questions 10-12 concern a study investigating the relationship between a student’s gender and whether
or not they skip class at least once a week. The following mosaic plot summarizes this relationship.
10. We know that there were more males surveyed than females because the black box is
taller for males.
TRUE
FALSE
11. In this sample, the proportion of males that skip class at least once a week is higher than
that of females.
TRUE
FALSE
12. The relative risk (RR) is 2.50. This means that the males in this sample are 2.5 times more
likely to skip class once a week than the females.
TRUE
FALSE
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Multiple Choice Questions: Circle the correct answer.
13. In one study on the effect of niacin on cholesterol level, 100 subjects who acknowledged being
longtime niacin takers had their cholesterol levels compared with those of 100 people who had never
taken niacin. In a second study, 50 subjects were randomly assigned to receive niacin and the other 50
to receive a placebo. Which of the following statements is correct?
a.
b.
c.
d.
The first study was a designed experiment, while the second was an observational study.
The first study was an observational study, while the second was a designed experiment.
Both studies were designed experiments.
Both studies were observational studies.
14. Consider a study on the smoking rates of seniors vs. freshmen at Winona Senior High School
(WSHS). The following hypotheses are examined:
Ho: psmoke|seniors = psmoke|freshman
Ha: psmoke|seniors ≠ psmoke|freshman
Suppose the p-value for this problem is .02. Using α = .05, which of the following is the most
correctly written conclusion?
a.
b.
c.
We have evidence that the proportion of freshman who smoke is different from the
proportion of seniors who smoke at WSHS.
We have evidence that the data supports the null hypothesis.
We have evidence that the proportion of freshman who smoke is NOT different from the
proportion of seniors who smoke at WSHS.
15. Suppose that from the smoking study mentioned in the previous problem, we observed from our
sample that 28% of freshmen smoked and that 15% of seniors smoked. Identify (by circling the label)
which of the following confidence intervals is most likely correct for psmoke|seniors - psmoke|freshman.
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16. In a survey of families in which both parents work, one of the questions asked was, “Have you
refused a job, promotion, or transfer because it would mean less time with your family?" Both men
and women were asked this question. Consider the following hypotheses and mosaic plot.
Ho: The proportion who responds “yes” does not differ across gender.
Ha: The proportion who responds “yes” differs across gender.
The p-value for this analysis is most likely to be which of the following?
a.
Less than α = .05 because the patterns for each row in the mosaic plot are similar across
the columns.
b. Greater than α = .05 because the patterns for each row in the mosaic plot are similar
across the columns.
c. Less than α = .05 because there are approximately twice as many females as males.
d. Greater than α = .05 because there are approximately twice as many females as males.
17. This table is based on results from a study investigating the use of an anti-seizure drug, Valproate, to
treat alcoholism. Subjects were randomly assigned to take either the drug or a placebo, and they
were questioned after 6 months to see if they had engaged in heavy drinking.
Drinking Behavior
Heavy Drinking
No heavy drinking
Totals
Drug
Valproate Placebo
14
15
18
7
32
22
Totals
29
25
54
A researcher hypothesizes that Valproate-takers will be less likely than placebo-takers to engage in
heavy drinking. Which of the following comparisons is most appropriate for supporting this
conclusion?
a.
b.
c.
d.
Compare the proportions 14/54 and 15/54.
Compare the proportions 14/29 and 18/25.
Compare the proportions 14/32 and 15/22.
Compare the numbers 14 and 15.
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18. This table is based on records of accidents compiled by a State Highway Safety and Motor Vehicles
Office. The Office wants to decide if people are less likely to have a fatal accident if they are wearing a
seatbelt than if they are not wearing a seatbelt. Which of the following comparisons is most
appropriate for supporting this conclusion?
Safety Equipment in Use
Seat belt
No seat belt
Totals
a.
b.
c.
d.
Injury
Nonfatal Fatal
412,368
510
162,527 1601
574,895 2,111
Totals
412,878
164,128
577,006
Compare the ratios 510/412,878 and 1,601/164,128
Compare the ratios 510/577,006 and 1,601/577,006
Compare the ratios 510/2,111 and 412.368/574,895
Compare the numbers 510 and 1,601
19. Some individuals are carriers of the bacterium Streptococcus pyogenes. To investigate whether there is
a relationship between carrier status and tonsil size in school children, 1105 children were examined
and classified according to their carrier status and tonsil size. The results are shown in the mosaic
plot below. Which of the following sets of statements follows from these results?
a.
b.
c.
We do not have evidence to show that there is a relationship between Tonsil Size and
Carrier Status
We have statistical evidence that there is a relationship between Tonsil Size and Carrier
Status. The data indicate that children who are carriers of Streptococcus pyogenes tend to
have larger tonsils.
We have statistical evidence that there is a relationship between Tonsil Size and Carrier
Status. The data indicate that children who are not carriers of Streptococcus pyogenes tend
to have larger tonsils.
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20. Suppose we used the data collected from the WSU student survey to test for a relationship between
gender and alcohol consumption. The observed counts are shown in the following contingency table.
If we were to find each of the expected counts needed to compute a chi-square test statistic, which of
the following would be the expected number of males who do consume alcohol?
a.
b.
c.
d.
106
111
87
88.94
21. The p-value for the previous study comparing alcohol assumption across gender is < .0001. Which of
the following is a valid conclusion?
a.
b.
c.
It would not be surprising to obtain the observed sample results if there is really no
difference between men and women.
It would be very surprising to obtain the observed sample results if there is really no
difference between men and women.
It would be very surprising to obtain the observed sample results if there is really a
difference between men and women.
22. The chi-square test is most appropriate for testing for a relationship between which of the following
variables?
a.
b.
c.
d.
Gender and Price paid for last haircut
Gender and Whether a subject is dieting to lose weight
Gender and Weight
Height and Weight
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Short Answer Questions:
23. The General Social Survey is a massive survey of American adults that is conducted yearly. In the
2006 survey, the researchers asked one question in two different forms (Form X and Form Y). About
half the people in this study were randomly assigned to Form X and the other half Form Y.
Form X: "Do you think we are spending too much, too little, or about the right amount of money on
improving the conditions of blacks in this country?"
Form Y: "Do you think we are spending too much, too little, or about the right amount of money on
assistance to blacks in this country?"
The two questions ask essentially the same thing, but in different words. However, of those given
Form X, 35% answered too little; of those given Form Y, only 25% answered too little.
Research Question: "Does the wording of the question have an effect on the responses of American
adults?"
a.
One variable of interest is whether the subjects in the study heard Form X or Form Y. Is this
variable categorical, or numeric?
b.
The other variable of interest is whether the subjects answered "too little", or not. Is this
variable categorical, or numeric?
c.
Which is the explanatory variable (i.e., the predictor) -- the one in a, or the one in b?
d. Complete the following sentence to explain why this was a designed experiment and not an
observational study. “The subjects were…”
e.
Set up the appropriate Ho and Ha for testing the research question of interest: "Does the
wording of the question have an effect the responses of American adults?"
Ho:
Ha:
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f.
Assume that the p-value from the appropriate analysis is < 0.0001. Write a conclusion in the
context of the problem.
24. The data in the following table describe results from a randomized clinical trial of the well-known
drug Viagra.
Treatment
Headache?
Yes
No
Viagra
117
617
Placebo
29
696
a.
Find the risk/chance of having a headache for those who take Viagra.
b.
Find the risk/chance of having a headache for those who take the placebo.
c.
Find the relative risk of having a headache for Viagra users versus placebo users.
d. Interpret the relative risk in the context of the problem.
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25. A study was conducted to investigate the relationship between smoking habits and divorce history of
1,669 people who had ever been married. The results are shown in the following table:
a. Estimate the risk or chance of divorce for smokers.
b. Estimate the risk or chance of divorce for non-smokers.
c. Find the relative risk of divorce (use the risk for smokers in the numerator).
d. Interpret this relative risk (RR) in the context of the problem.
e. A 95% confidence interval for the RR is given by (1.37, 1.75). Does this interval suggest there is
increased risk for divorce associated with smoking? Explain your reasoning.
f. Even if the results of this study indicate that a smoker is more likely to divorce, can this study be used
to imply that smoking causes divorce? Explain your reasoning.
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26. This table is based on results from the 2002 General Social Survey. A researcher hypothesizes that
males are more likely to favor the death penalty than females.
a. Which of the following comparisons is most appropriate for supporting this conclusion?
A. Compare the proportions 475/1308 and 424/1308.
B. Compare the proportions 475/899 and 156/409.
C. Compare the proportions 475/631 and 424/677.
D. Compare the numbers 475 and 424.
b. The 95% confidence interval for the difference in proportions P(favor death penalty|female) – P(favor
death penalty|male) is given by (-.17, -.08). Which of the following conclusions is most appropriate?
A. This interval provides evidence that the proportion of females who favor the death penalty is greater
than the proportion of males that favor the death penalty.
B. This interval provides evidence that the proportion of males who favor the death penalty is greater
than the proportion of females that favor the death penalty.
C. This interval provides no evidence that the proportion who favor the death penalty differs across
gender.
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