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Chapter 9
STT 201
STATISTICAL METHODS
TAKE HOME MIDTERM EXAMINATION IV
DUE DATE: TUESDAY NOVEMBER 25, 2014
SCANTRONS WILL BE PROVIDED DURING THE CLASS MEETING BEFORE THE
DUE DATE
EARLY SUBMISSION: IF YOU SUBMIT YOUR WORK ON OR BEFORE THURSDAY
NOVEMBER 13, 2014, YOU EARN AN EXTRA 4 POINTS.
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Chapter 9
1. Which of the following statements is correct about a parameter and a statistic associated with
repeated random samples of the same size from the same population?
A. Values of a parameter will vary from sample to sample but values of a statistic will not.
B. Values of both a parameter and a statistic may vary from sample to sample.
C. Values of a parameter will vary according to the sampling distribution for that parameter.
D. Values of a statistic will vary according to the sampling distribution for that statistic.
E. None of the above
2. Which of the following statements best describes the relationship between a parameter and a
statistic?
A. A parameter has a sampling distribution with the statistic as its mean.
B. A parameter has a sampling distribution that can be used to determine what values the
statistic is likely to have in repeated samples.
C. A parameter is used to estimate a statistic.
D. A statistic is used to estimate a parameter.
E. None of the above
3. Which one of the following statements is false?
A. The standard error measures the variability of a population parameter.
B. The standard error of a sample statistic measures, roughly, the average difference
between the values of the statistic and the population parameter.
C. Assuming a fixed value of s = sample standard deviation, the standard error of the mean
decreases as the sample size increases.
D. The standard error of a sample proportion decreases as the sample size increases.
E. None of the above
4. Which one of the following statements is false?
A. A sampling distribution is the probability distribution of a sample statistic. It describes
how values of a sample statistic vary across all possible random samples of a specific
size that can be taken from a population.
B. For all five scenarios considered, the sampling distribution is approximately normal as
long as the sample size(s) are large enough.
C. The mean value of a sampling distribution is the mean value of a sample statistic over all
possible random samples. For the five scenarios, this mean equals the value of the
statistic.
D. The standard deviation of a sampling distribution measures the variation between all
possible values of the sample statistic and their mean over all possible random samples.
For the five scenarios, this mean equals the value of the parameter.
E. None of the above
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Chapter 9
5. A comparison is to be made between the proportion of second graders that cannot read at
second grade level and the proportion of third graders that cannot read at second grade level.
School records from schools across the state are collected and records for 123 second graders
and 146 third graders are randomly selected. Of the sampled second graders, 25 seem to be
not reading at second grade level. Of the sample third graders, 26 do not read at second grade
level.
What is the correct notation for the difference
A. 1  2
B. x1  x2
C. p1  p2
D. pˆ 1  pˆ 2
E. None of the above
25
 26
123 146
?
6. If the size of a sample randomly selected sample from a population is increased from n = 100
to n = 400, then the standard deviation of p̂ will
A. remain the same.
B. increase by a factor of 4.
C. decrease by a factor of 4.
D. decrease by a factor of 2.
E. None of the above
7. The mean of the sampling distribution for a sample proportion depends on the value(s) of
A. the true population proportion but not the sample size.
B. the sample size but not the true population proportion.
C. the sample size and the true population proportion.
D. neither the sample size nor the true population proportion.
E. None of the above
Questions 8 – 10
A television station plans to ask a random sample of 400 city residents if they can name the
news anchor on the evening news at their station. They plan to fire the news anchor if fewer than
10% of the residents in the sample can do so. Suppose that in fact 12% of city residents could
name the anchor if asked.
8. What is the mean of the sampling distribution for the sample proportion of city residents who
can name the news anchor on the evening news at their station?
A. 400
B. 0.10
C. 0.12
D. 48
E. None of the above
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Chapter 9
9. What is the standard deviation of the sampling distribution for the sample proportion of city
residents who can name the news anchor on the evening news at their station?
A. 0.015
B. 0.0162
C. 0.1056
D. 0.12
E. None of the above
10. What is the approximate probability that the anchor will be fired?
A. 0.02
B. 1.23
C. 0.11
D. 0.89
E. None of the above
11. Suppose that the mean of the sampling distribution for the difference in two sample
proportions is 0. This tells us that
A. The two sample proportions are both 0.
B. The two sample proportions are equal to each other.
C. The two population proportions are both 0.
D. The two population proportions are equal to each other.
E. None of the above
Questions 12 – 14
A new study finds that frequent use of painkillers does not substantially increase a healthy man's
risk of developing hypertension (high blood pressure). In other words, the proportion of healthy
men with hypertension is the same for those who use painkillers frequently and those who don’t.
According to the American Heart Association, 1 in 3 American adults have hypertension.
12. Which of the following choices correctly denotes the difference between the proportions of
men with hypertension (frequent use of painkillers – not frequent use of painkillers)?
A. p1  p2  1 / 3
B. p1  p2  0
C. pˆ 1  pˆ 2  1 / 3
D. None of the above.
E. None of the above
13. Suppose random samples of 200 men who use painkillers frequently and 200 men who don’t
are to be selected. What is the standard deviation for the difference between the two sample
proportions?
A. 0
B. 0.0333
C. 0.0471
D. 0.5773
E. None of the above
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Chapter 9
14. Suppose random samples of 200 men who use painkillers frequently and 200 men who don’t
are to be selected. What is probability that the difference between the two sample proportions
(frequent use of painkillers – not frequent use of painkillers) is greater than 10 percentage
points (0.10)?
A. 0.0013
B. 0.0169
C. 0.0337
D. 0.9999
E. None of the above
15. Which of the following statements is true about the standard deviation of x ?
A. It decreases as the sample size n increases.
B. It increases as the sample size n increases.
C. It does not change as the sample size n increases.
D. It changes each time a new sample is drawn.
E. None of the above
16. The standard deviation of the sampling distribution for a sample mean depends on the
value(s) of
A. the sample size and the population standard deviation.
B. the sample size but not the population standard deviation.
C. the population standard deviation but not the sample size
D. neither the sample size nor the population standard deviation.
E. None of the above
17. Consider a random sample with sample mean x . If the sample size is increased from n = 40
to n = 360, then the standard deviation of x will
A. remain the same.
B. increase by a factor of 9 (will be multiplied by 9).
C. decrease by a factor of 9 (will be multiplied by 1/9).
D. decrease by a factor of 3 (will be multiplied by 1/3).
E. None of the above
18. A store manager is trying to decide whether to price oranges by weight, with a fixed cost per
pound, or by the piece, with a fixed cost per orange. He is concerned that customers will
choose the largest ones if there is a fixed price per orange. For one week the oranges are
priced by the piece rather than by weight, and during this time the mean weight of the
oranges purchased is recorded for all customers who buy 4 of them. The manager knows the
population of weights of individual oranges is bell-shaped with mean of 8 ounces and a
standard deviation of 1.6 ounces. If the 4 oranges each customer chooses are equivalent to a
random sample, what should be the approximate mean and standard deviation of the
distribution of the mean weight of 4 oranges?
A. mean = 32 ounces, standard deviation = 6.2 ounces
B. mean = 8 ounces, standard deviation = 1.6 ounces
C. mean = 8 ounces, standard deviation = 0.8 ounces
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Chapter 9
D. mean = 2 ounces, standard deviation = 0.4 ounces
E. None of the above
19. In the population of male students, motivation scores follow a normal distribution with an
average of 32.4 and a standard deviation of 7. A random sample of 16 male students is to be
taken. They are all asked to answer the motivation questionnaire so that their motivation
scores can be determined. What is the probability that the sample mean score will exceed 35?
A.
B.
C.
D.
E.
< 0.0001
0.0681
0.1977
0.3557
None of the above
Questions 20 – 22
Exam scores for a large introductory statistics class follow an approximate normal distribution
with an average score of 56 and a standard deviation of 5. The average exam score in your lab
was 59.5. The 20 students in your lab sections will be considered a random sample of all students
who take this class.
20. What is the expected value of the average exam score of the 20 students in your lab section?
A. 5
B. 20
C. 56
D. 59.5
E. None of the above
21. What is the standard deviation of the distribution of the average exam score of the 20
students in your lab section?
A. 0.25
B. 1.12
C. 1.25
D. 5
E. None of the above
22. What is the probability that the average score of a random sample of 20 students exceeds
59.5?
A. < 0.0001
B. 0.0009
C. 0.0026
D. 0.2420
E. None of the above
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Chapter 9
Questions 23 – 26
High school students can be categorized into two groups by the amount of activities they are
involved in. Let group 1 consist of all high school students who are very involved in sports and
other activities and group 2 consist of all high school students who aren’t. The distributions of
GPAs in both groups are approximately normal. The mean and standard deviation for group 1 are
2.9 and 0.4, respectively. The mean and standard deviation for group 2 are 2.7 and 0.5,
respectively. Independent random samples of 50 high school students are to be selected from
both groups (for a total of 100 students).
23. If the sample mean GPA is to be calculated for both groups and we calculate the difference
as involved in activities – not so involved in activities, what is the expected value for the
difference in sample means?
A. 0
B. 0.2
C. 0.4
D. 0.6
E. None of the above
24. If the sample mean GPA is to be calculated for both groups and we calculate the difference
as involved in activities – not so involved in activities, what is the standard deviation of the
sampling distribution of the difference in sample means?
A. 0.0082
B. 0.0905
C. 0.18
D. 0.45
E. None of the above
25. What is the probability that the average GPA in the sample of students who are not so
involved is higher than the average GPA in the sample of students who are very involved?
A. < 0.0001
B. 0.0136
C. 0.0582
D. 0.9864
E. None of the above
26. What is the probability that the average GPAs in the two samples differ by no more than 0.1?
A. 0.1341
B. 0.2266
C. 0.2415
D. 0.8659
E. None of the above
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Chapter 9
27. Which statement is not true about confidence intervals?
A. A confidence interval is an interval of values computed from sample data that is likely to
include the true population value.
B. An approximate formula for a 95% confidence interval is sample estimate  margin of
error.
C. A confidence interval between 20% and 40% means that the population proportion lies
between 20% and 40%.
D. A 99% confidence interval procedure has a higher probability of producing intervals that
will include the population parameter than a 95% confidence interval procedure.
E. All of the above
28. Which statement is not true about the 95% confidence level?
A. Confidence intervals computed by using the same procedure will include the true
population value for 95% of all possible random samples taken from the population.
B. The procedure that is used to determine the confidence interval will provide an interval
that includes the population parameter with probability of 0.95.
C. The probability that the true value of the population parameter falls between the bounds
of an already computed confidence interval is roughly 95%.
D. If we consider all possible randomly selected samples of the same size from a population,
the 95% is the percentage of those samples for which the confidence interval includes the
population parameter.
E. All of the above
Questions 29 – 31
A randomly selected sample of 400 students at a university with 15-week semesters was asked
whether or not they think the semester should be shortened to 14 weeks (with longer classes).
Forty-six percent of the 400 students surveyed answered yes.
29. Which one of the following statements about the number 46% is correct?
A. It is a sample statistic.
B. It is a population parameter.
C. It is a margin of error.
D. It is a standard error.
E. None of the above
30. Which one of the following description of the number 46% is not correct?
A. point estimate
B. population parameter
C. sample estimate
D. sample statistic
E. None of the above
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Chapter 9
31. The multiplier for a confidence interval is determined by
A. the desired level of confidence and the sample size.
B. the desired level of confidence but not the sample size.
C. the sample size but not the desired level of confidence.
D. neither the sample size nor the level of confidence.
E. None of the above
Questions 32 – 35
In a survey of n = 950 randomly selected individuals, 17% answered yes to the question “Do you
think the use of marijuana should be made legal or not?”
32. A 95% confidence interval for the proportion of all Americans in favor of legalizing
marijuana is
A. 0.150 to 0.190
B. 0.146 to 0.194
C. 0.142 to 0.198
D. 0.139 to 0.201
E. None of the above
33. A 90% confidence interval for the proportion of all Americans in favor of legalizing
marijuana is
A. 0.150 to 0.190
B. 0.146 to 0.194
C. 0.142 to 0.198
D. 0.139 to 0.201
E. None of the above
34. A 98% confidence interval for the proportion of all Americans in favor of legalizing
marijuana is
A. 0.150 to 0.190
B. 0.146 to 0.194
C. 0.142 to 0.198
D. 0.139 to 0.201
E. None of the above
35. A 99% confidence interval for the proportion of all Americans in favor of legalizing
marijuana is
A. 0.150 to 0.190
B. 0.146 to 0.194
C. 0.142 to 0.198
D. 0.139 to 0.201
E. None of the above
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Chapter 9
Questions 36 – 38
A 95% confidence interval for the proportion of young adults who skip breakfast is found to be
0.20 to 0.27.
36. Which of the following is a correct interpretation of the 95% confidence level?
A. There is a 95% probability that the true proportion of young adults who skip breakfast is
between 0.20 and 0.27.
B. In about 95% of all studies for which this procedure is used, the confidence interval will
cover the true population proportion, but there is no way to know if this interval covers
the true proportion or not.
C. If this study were to be repeated with a sample of the same size, there is a 95%
probability that the sample proportion would be between 0.20 and 0.27.
D. The proportion of young adults who skip breakfast 95% of the time is between 0.20 and
0.27.
E. None of the above
37. Which of the following is the correct interpretation of the 95% confidence interval?
A. There is a 95% probability that the proportion of young adults who skip breakfast is
between 0.20 and 0.27.
B. If this study were to be repeated with a sample of the same size, there is a 95%
probability that the sample proportion would be between 0.20 and 0.27.
C. We can be 95% confident that the sample proportion of young adults who skip breakfast
is between 0.20 and 0.27.
D. We can be 95% confident that the population proportion of young adults who skip
breakfast is between 0.20 and 0.27.
E. None of the above
38. From the information provided, we can determine that ANS = A
A. p̂ = 0.235 and margin of error = 0.035.
B. p̂ = 0.235 and margin of error = 0.07.
C. p = 0.235 and margin of error = 0.035.
D. p = 0.235 and margin of error = 0.07.
E. None of the above
39. Suppose that 90%, 95%, 98%, and 99% confidence intervals are computed (using the same
sample) for a population proportion. Which confidence level will give the narrowest interval?
A. 99%
B. 98%
C. 95%
D. 90%
E. None of the above
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Chapter 9
40. You plan to use a conservative margin of error of 2%. How large a sample size do you need?
A. 100
B. 400
C. 2500
D. None of the above
E. None of the above
41. Which of the following is the minimum sample size that could be used to guarantee that the
margin of error for a confidence interval for a proportion is no more than 0.025?
A. 100
B. 400
C. 1600
D. 2500
E. None of the above
Questions 42 and 44
Random samples from two age groups of brides (200 brides under 18 years and 100 brides at
least twenty years old) showed that 50% of brides in the under 18 group were divorced after 15
years, while 40% of brides in the 20 or older age group were divorced after 15 years. The
difference between the two proportions is 0.10, with a standard error of 0.0604.
42. What is a 95% confidence interval for the difference between the population proportions of
brides who are divorced within 15 years (brides under 18  brides at least 20)?
A. (0.018, 0.218)
B. (0.123, 0.023)
C. (0.040, 0.160)
D. None of the above
E. None of the above
43. What is a 99% confidence interval for the difference between the population proportions of
brides who are divorced within 15 years (brides under 18  brides at least 20)?
A. (0.123, 0.023)
B. (0.056, 0.256)
C. (0.040, 0.160)
D. None of the above
E. None of the above
44. In a recent poll of 500 13-year-olds, many indicated to enjoy their relationships with their
parents. Suppose that 200 of the 13-year olds were boys and 300 of them were girls. We
wish to estimate the difference in proportions of 13-year old boys and girls who say that their
parents are very involved in their lives. In the sample, 93 boys and 172 girls said that their
parents are very involved in their lives. What is a 96% confidence interval for the difference
in proportions (proportion of boys minus proportion of girls)?
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Chapter 9
A.
B.
C.
D.
E.
(0.2015, 0.0151)
(0.1973, 0.0194)
(0.1978, 0.0289)
None of the above
None of the above
45. The following ranges are possible 95% confidence intervals for the percentage of Americans
who think they work too many hours. For which one of the confidence intervals could you
conclude that a majority of the population thinks they work too many hours?
A. 41% to 49%
B. 49% to 54%
C. 42% to 51%
D. 52% to 58%
E. None of the above
46. In a past General Social Survey, a random sample of men and women answered the question
“Are you a member of any sports groups?” Based on the sample data, 95% confidence
intervals for the population proportion who would answer yes are 0.13 to 0.19 for women and
0.25 to 0.33 for men. Based on these results, you can reasonably conclude that
A. at least 25% of American men and American women belong to sports clubs.
B. there is no conclusive evidence of a gender difference in the proportions of men and
women who belong to sports clubs.
C. there is conclusive evidence of a gender difference in proportions of American men and
American women who belong to sports clubs.
D. None of the above
E. None of the above
47. A CBS News poll taken in January 2010 asked a random sample of 1,090 adults in the US
"Do you think the federal government is adequately prepared to deal with a major earthquake
in the United States, or not?" A 95% confidence interval for the proportion of the population
that thinks the government is prepared is .31 to .37. Based on this result, which one of the
following statements is false?
A. It is reasonable to say that a majority of adults in the US think the federal government is
prepared to deal with a major earthquake.
B. It is reasonable to say that fewer than half of adults in the US think the federal
government is prepared to deal with a major earthquake.
C. It is possible that approximately 35% of adults in the US think the federal government is
prepared to deal with a major earthquake.
D. A 99% confidence interval for the proportion of the population that thinks the
government is prepared would be wider than the 95% confidence interval given above.
E. None of the above
FOR QUESTIONS 48 – 80, READ CHAPTER 4, PAGES 124 – 134, AND CHAPTER 15,
PAGES 599 – 610. YOU HAVE TO STUDY THESE PAGES INDEPENDENTLY.
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Chapter 9
48. A student survey was done to study the relationship between class standing (freshman,
sophomore, junior, or senior) and major subject (English, Biology, French, Political Science,
Undeclared, or Other). What are the degrees of freedom for the chi-square statistic?
A. 24
B. 20
C. 15
D. 5
E. None of the above
49. A chi-square statistic was computed for a two-way table having 4 degrees of freedom. The
value of the statistic was 9.49. What is the p-value?
A. 0.005
B. 0.001
C. 0.01
D. 0.4
E. None of the above
50. A chi-square statistic was computed for a two-way table having 20 degrees of freedom. The
value of the statistic was 30.00. What is the p-value or p-value range?
A. p-value = 0.05
B. 0.05 < p-value < 0.075
C. 0.025 < p-value < 0.05
D. None of the above
E. None of the above
51. Suppose that the chi-square statistic equals 10.9 for a two-way table with 4 rows and 2
columns. In which range does the approximate p-value fall for this situation?
A. Less than 0.001
B. Between 0.01 and 0.025
C. Between 0.025 and 0.05
D. Between 0.10 and 0.25
E. None of the above
52. Which one of the following is NOT true about the table of expected counts for a chi-square
test?
A. The expected counts are computed assuming the null hypothesis is true.
B. The expected counts are computed assuming the alternative hypothesis is true.
C. The expected counts have the same row and column totals as the observed counts.
D. The pattern of row percents is identical for all rows of expected counts.
E. None of the above
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Chapter 9
53. A chi-square test involves a set of counts called “expected counts.” What are the expected
counts?
A. Hypothetical counts that would occur if the alternative hypothesis were true.
B. Hypothetical counts that would occur if the null hypothesis were true.
C. The actual counts that did occur in the observed data.
D. The long-run counts that would be expected if the observed counts are representative.
E. None of the above
54. Which of the following gives statistically significant results at the 0.01 level of significance?
A.  2  9.1, df = 2
B.  2  5.3, df = 1
C.  2  13.8, df = 4
D.  2  14.1, df = 5
E. None of the above
55. Suppose that a two-way table displaying sample information about gender and opinion about
the legalization of marijuana (yes or no) is examined using a chi-square test. The necessary
conditions are met and the chi-square value is calculated to be 15. What conclusion can be
made?
A. Gender and opinion have a statistically significant relationship
B. Gender and opinion do not have a statistically significant relationship
C. It is impossible to make a conclusion because we don’t know the sample size.
D. It is impossible to make a conclusion because we don’t know the degrees of freedom.
E. None of the above
56. Which of the following relationships could be analyzed using a chi-square test?
A. The relationship between height (inches) and weight (pounds).
B. The relationship between satisfaction with K-12 schools (satisfied or not) and political
party affiliation.
C. The relationship between gender and amount willing to spend on a stereo system (in
dollars).
D. The relationship between opinion on gun control and income earned last year (in
thousands of dollars).
E. None of the above
57. For which of the following tests is the null hypothesis not of the form parameter = null
value?
A. A test for the difference in two proportions.
B. A test for the mean of paired differences.
C. A test for the difference in means for independent samples.
D. A chi-square test of independence.
E. None of the above
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Chapter 9
Questions 58 to 62
In the General Social Survey, respondents were asked what they thought was most important to
get ahead: hard work, lucky breaks, or both. Minitab output for 1026 respondents, by gender, is
shown below:
Expected counts are printed below observed counts
Male
284
292.31
Female
393
384.69
Total
677
Lucky breaks
84
88.51
121
116.49
205
Both
75
62.18
69
81.82
144
443
583
1026
Hard work
Total
Chi-Sq = 0.236 + 0.180 + 0.230 + 0.175 + 2.645 + 2.010 = 5.476
P-Value = 0.065
58. What is the null hypothesis for this situation?
A. There is a relationship between gender and opinion on what is important to get ahead in
the sample.
B. There is no relationship between gender and opinion on what is important to get ahead in
the sample.
C. There is a relationship between gender and opinion on what is important to get ahead in
the population.
D. There is no relationship between gender and opinion on what is important to get ahead in
the population.
E. None of the above
59. What is the alternative hypothesis for this situation?
A. There is a relationship between gender and opinion on what is important to get ahead in
the sample.
B. There is no relationship between gender and opinion on what is important to get ahead in
the sample.
C. There is a relationship between gender and opinion on what is important to get ahead in
the population.
D. There is no relationship between gender and opinion on what is important to get ahead in
the population.
E. None of the above
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Chapter 9
60. What is the value of the test statistic?
A. 443
B. 583
C. 5.476
D. None of the above
E. None of the above
61. What are the degrees of freedom for the test statistic?
A. 2
B. 3
C. 4
D. None of the above
E. None of the above
62. At a significance level of 0.05, what is the conclusion?
A. Reject the null hypothesis and conclude there is no relationship between the variables.
B. Reject the null hypothesis and conclude there is a relationship between the variables.
C. Do not reject the null hypothesis and conclude the evidence is not strong enough to show
a relationship between the two variables.
D. Do not reject the null hypothesis and conclude there is a relationship between the
variables.
E. None of the above
Questions 63 to 66: A researcher conducted a study on college students to see if there was a
link between gender and how often they have cheated on an exam. She asked two questions on a
survey:
(1) What is your gender? Male ___ Female ___
(2) How many times have you cheated on an exam while in college?
Never __ 1 or 2 times ___ 3 or more times ___
A two-way table of observed counts follows:
Gender
Never
Male
Female
Total
60
60
120
Cheated on an exam?
1 or 2 times
3 or more
times
20
20
30
10
50
30
Total
100
100
200
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63. Considering the researcher’s objectives, what is the appropriate null hypothesis to test?
A. p = 0.50 where p = probability of answering "Never" to question (2) on the survey.
B. There is a difference between males and females with regard to the distribution of
responses.
C. There is no relationship between the two variables.
D. There is a relationship between the two variables.
E. None of the above
64. What are the degrees of freedom for the test statistic?
A. 6
B. 5
C. 3
D. 2
E. None of the above
65. How many female students would you expect to have cheated once or twice if the null
hypothesis were true?
A. 20
B. 25
C. 30
D. 50
E. None of the above
66. The value of the χ2-test statistic is 5.33. Are the results statistically significant at the 5%
significance level?
A. Yes, because 5.33 is greater than the critical value of 3.84.
B. Yes, because 5.33 is greater than the critical value of 4.01.
C. No, because 5.33 is smaller than the critical value of 5.99.
D. No, because 5.33 is smaller than the critical value of 11.07.
E. None of the above
Questions 67 – 70
Students in a statistics class were asked, “With whom do you find it easier to make friends:
person of the same sex, person of opposite sex, or no preference?” A table summarizing the
responses by gender is given below. Minitab results for a chi-square test for these data were
“Chi-Sq = 7.15 p-value = 0.028.”
Gender
Male
Female
Total
With whom is it easier to make friends?
no
opposite
same
Total
preference
sex
sex
40
50
30
120
40
20
20
80
80
70
50
200
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67. What is the null hypothesis for this situation?
A. The variables “gender” and “with whom is it easier to make friends?” are dependent in
the population.
B. There is a relationship between gender and whom it is easier to make friends with in the
population.
C. The distribution of the answers to the question “with whom is it easier to make friends?”
for male students differ from that of the female students.
D. There is no relationship between gender and whom it is easier to make friends with in the
population.
E. None of the above
68. What percentage of female students think it is easier to make friends with a girl?
A. 15%
B. 25%
C. 30%
D. 60%
E. None of the above
69. What is the expected number of female students who think it is easier to make friends with a
girl, if the null hypothesis were true?
A. 20
B. 25
C. 30
D. 32
E. None of the above
70. What are the degrees of freedom for this situation?
A. 2
B. 3
C. 4
D. 5
E. None of the above
Questions 71 – 73
The table below shows the opinions of 321 respondents from the General Social Survey by
whether they owned a gun (or not) and whether they favored (or opposed) a law requiring a
permit to own a gun.
Own Gun?
Yes
No
Total
Gun Law Opinion
Oppose
Favor
35
110
20
156
55
266
Total
145
176
321
Chi-Square = 9.137, DF = 1, P-Value = 0.003
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71. The percentage of gun owners in favor of the gun law was
A. 34%
B. 41%
C. 76%
D. 83%
E. None of the above
72. The percentage of non-gun owners in favor of the gun law was
A. 49%
B. 59%
C. 83%
D. 89%
E. None of the above
73. Based on the chi-square statistic and p-value, one can conclude that
A. the difference between the support for the gun law between gun owners and non-gun
owners is not statistically significant.
B. the difference between the support for the gun law between gun owners and non-gun
owners is statistically significant.
C. the difference between the support for the gun law between gun owners and non-gun
owners is not practically significant.
D. the difference between the support for the gun law between gun owners and non-gun
owners is practically significant.
E. None of the above
74. A study done by the Center for Academic Integrity at Rutgers University surveyed 2116
students at 21 colleges and universities. Some of the schools had an "honor code" and others
did not. Of the students at schools with an honor code, 7% reported having plagiarized a
paper via the Internet, while at schools with no honor code, 13% did so. (Sacramento Bee,
Feb 29, 2000, D1.) Although the data provided are not sufficient to carry out a chi-square test
of the relationship between whether or not a school has an honor code and whether or not a
student would plagiarize a paper via the Internet, suppose such a test were to show a
statistically significant relationship on the basis of this study. What would be the correct
conclusion?
A. Because this is an observational study, it can be concluded that implementing an honor
code at a college or university will reduce the risk of plagiarism.
B. Because this is a randomized experiment, it can be concluded that implementing an
honor code at a college or university will reduce the risk of plagiarism.
C. Because this is an observational study and confounding variables are likely, it cannot be
concluded that implementing an honor code at a college or university will reduce the risk
of plagiarism.
D. Because this is a randomized experiment and confounding variables are likely, it cannot
be concluded that implementing an honor code at a college or university will reduce the
risk of plagiarism.
E. None of the above
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Chapter 9
Questions 75 – 77
In the General Social Survey, respondents were asked “If your party nominated a woman for
President, would you vote for her if she were qualified for the job?” Minitab output for 953
respondents, by race, is shown below:
Expected counts are printed below observed counts
white
713
709.00
black
82
84.84
other
30
31.16
Total
825
no
106
110.00
16
13.16
6
4.84
128
Total
819
98
36
953
yes
Chi-Sq = 0.023 +
1.199
P-Value = 0.549
0.095 +
0.044 + 0.146 +
0.612 +
0.281 =
75. What is the null hypothesis for this situation?
A. There is a relationship between race and opinion on voting for a female president in the
sample.
B. There is no relationship between race and opinion on voting for a female president in the
sample.
C. There is a relationship between race and opinion on voting for a female president in the
population.
D. There is no relationship between race and opinion on voting for a female president in the
population.
E. Null Hypothesis = P - Value
76. What is the alternative hypothesis for this situation?
A. There is a relationship between race and opinion on voting for a female president in the
sample.
B. There is no relationship between race and opinion on voting for a female president in the
sample.
C. There is a relationship between race and opinion on voting for a female president in the
population.
D. There is no relationship between race and opinion on voting for a female president in the
population.
E. Alternative Hypothesis = P - Value
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Chapter 9
77. At a significance level of 0.05, what is the conclusion?
A. Reject the null hypothesis and conclude there is no relationship between the variables.
B. Reject the null hypothesis and conclude there is a relationship between the variables.
C. Do not reject the null hypothesis and conclude the evidence is not strong enough to show
a relationship between the two variables.
D. Do not reject the null hypothesis and conclude there is a relationship between the
variables.
E. No valid conclusion can be drawn.
78. The statistical significance of the association or relationship between two categorical
variables is examined using a value known as the chi-square statistic, and a corresponding pvalue that assesses the chance of getting this value for the Chi-square statistic or one even
larger. Suppose the p-value of the test turns out to be 0.18. In this case, we should decide
that
A. there is only an 18% chance that the observed relationship occurred by chance, so we can
say that the relationship is statistically significant.
B. the observed relationship most likely did not occur by chance, so we can say that the
relationship is statistically significant.
C. the observed relationship most likely did not occur by chance, so we cannot say that the
relationship is statistically significant.
D. the observed relationship could have occurred by chance, so we cannot say that the
relationship is statistically significant.
E. None of the above
79. A statistically significant relationship between two categorical variables is illustrated in the
sample as one that
A. is small enough that it is likely to have occurred in the observed sample even if there is
no relationship in the population.
B. is small enough that it is unlikely to have occurred in the observed sample if there is no
relationship in the population.
C. is large enough that it is likely to have occurred in the observed sample even if there is no
relationship in the population
D. is large enough that it is unlikely to have occurred in the observed sample if there is no
relationship in the population.
E. None of the above
80. What is the primary purpose of doing a chi-square test?
A. to determine if there is a significant relationship between two quantitative variables
B. to determine if there is a significant relationship between two categorical variables
C. to determine if there is a significant relationship between two continuous variables
D. to estimate a population proportion
E. None of the above
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