Inference Review 3 - Chapter 11
Multiple Choice
Scenario 11-7
Assigned
Treatment
Arrest
Citation
Advise/Separate
None
175
181
187
Number of re-arrests
One
Two
36
2
33
7
24
1
Three or more
1
3
0
When a police officer responds to a call for help in a case of spousal abuse, what should the officer do? A randomized controlled experiment in
Charlotte, North Carolina, studied three police responses to spousal abuse: advise and possibly separate the couple, issue a citation to the offender,
and arrest the offender. The effectiveness of the three responses was determined by re-arrest rates. The table below shows these rates.
1. Use Scenario 11-7. Even though Puerto Rico is a territory of the United States, there are many cultural differences
between the states on the continent of North America and the Caribbean island of Puerto Rico. These differences include the way consumers respond
to problems with purchases. Two researchers surveyed owners of VCRs in the Northeastern United States and in Puerto Rico. They asked those who
had experienced problems with their VCRs and whether they had complained. The results are given in the table below.
Region
N.E. United States
Puerto Rico
Complained?
Yes
No
330
94
64
33
The cell that contributes most to the 2 statistic is
A. Americans in the Northeastern United States who complained. B. Puerto Ricans who complained. C. Americans in the Northeastern United
States who did not complain. D. Since the data form a 2  2 table, all cells contribute equally to the statistic. E. Puerto Ricans who did not
complain.
2. Use Scenario 11-7. Suppose we wish to test the null hypothesis that the proportion of subsequent arrests is the same regardless of the treatment
assigned. Which of the following statements is true?
A. We cannot test this hypothesis because this is an experiment, not a random sample. B. The test of the null hypothesis will have a very small Pvalue (below 0.0001) because there were so few cases where there was more than one re-arrest. C. We should eliminate the last column, since there
are so few entries in that column. D. The test of the null hypothesis will have a very small P-value (below 0.0001) because the counts in each row
are not identical. E. We cannot test this hypothesis because the expected cell counts are less than 5 in some of the cells.
Scenario 11-8 All current-carrying wires produce electromagnetic (EM) radiation, including the electrical wiring running into, through, and out of
our homes. High-frequency EM radiation is thought to be a cause of cancer; the lower frequencies associated with household current are generally
assumed to be harmless. To investigate this, researchers visited the addresses of children in the Denver area who had died of some form of cancer
(leukemia, lymphoma, or some other type. and classified the wiring configuration outside the building as either a high-current configuration (HCC. or
as a low-current configuration (LCC.. Here are some of the results of the study.
Cancer type
Leukemia
Lymphoma
Other cancers
HCC
52
10
17
LCC
84
21
31
Computer software was used to analyze the data. The output is given below. It includes the cell counts, the expected cell counts, and the value of the
2 statistic. In the table, expected counts are printed below observed counts.
HCC
LCC
TOTAL
Chi-Sq = 0.435
Leukemia
52
49.97
84
86.03
136
Lymphoma
10
11.39
21
19.61
31
Other Cancers
17
17.64
31
30.36
48
Total
79
136
215
3. Use Scenario 11-8. Which of the following intervals contains the P-value of the test?
A. between 0.05 and 0.10. B. between 0.01 and 0.05. C. between 0.10 and 0.20. D. less than 0.01. E. larger than 0.20.
4. Use Scenario 11-8. The appropriate degrees of freedom for the 2 statistic is
A. 2. B. 5. C. 1. D. 4. E. 3.
5. Use Scenario 11-8. Which of the following may we conclude, based on the test results?
A. There is weak evidence that HCC causes cancer in children. B. There is not much evidence of an association between wiring configuration and
the type of cancer that caused the deaths of children in the study. C. Leukemia is the most common type of cancer among children. D. HCC either
causes cancer directly or is a major contributing factor to the development of cancer in children. E. There is strong evidence of an association
between wiring configuration and the chance a child will develop some form of cancer.
Scenario 11-2 To test the effectiveness of a certain computer software’s random number generator, I randomly select 1000 numbers from a standard
Normal distribution. I classify these 1000 numbers according to whether their values are at most –2, between –2 and 0, between 0 and 2, or at least 2.
The results are given in the following table. The expected counts, based on the 68-95-99.7 rule, are given as well.
Observed Count
18
492
468
22
Expected Count
25
475
475
25
To test to see if the distribution of observed counts differs significantly from the distribution of expected counts, we use a 2 test.
6. Use Scenario 11-2. The value of the 2 statistic is found to be 3.03. The P-value of the test is
A. between 0.10 and 0.20. B. between 0.01 and 0.05. C. less than 0.01. D. greater than 0.20. E. between 0.05 and 0.10.
7. Use Scenario 11-2. For this test, the 2 statistic has approximately a chi-square (2) distribution. How many degrees of freedom does this
distribution have?
A. 1000. B. 4. C. 999. D. 7. E. 3.
Scenario 11-9 Recent revenue shortfalls in a Midwestern state led to a reduction in the state budget for higher education. To offset the reduction, the
largest state university proposed a 25% tuition increase. It was determined that such an increase was needed simply to compensate for the lost support
from the state. Random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether or not they were
strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university’s budget at current levels. The results
are given in the following table.
Year
Freshman
Sophomore
Junior
Senior
Strongly
Yes
39
36
29
18
Opposed?
No
11
14
21
32
8. Use Scenario 11-9. Which of the following are conditions that must be met before performing a chi-square test on these data?
I. The sample is large enough so that all observed counts are greater than 5.
II. The data come from independent random samples of Freshmen, Sophomores, Juniors, and Seniors.
III. The populations from which the samples were taken are Normally distributed.
A. I only B. II only C. All three conditions must be met. D. III only E. I and III only
Scenario 11-4
Cookie Brand
Number of choosing brand
A
26
B
18
C
24
D
28
Ida wants to know if people show a preference for one brand of ready-made chocolate chip cookie dough over another. To test this, she bakes eight
dozen cookies from dough made by each of four manufacturers which she labels brands A, B, C, and D, to conceal the name of the company from the
tasters. She then selects a simple random sample of 96 students at her school to try each brand of cookie and choose the brand they like best. The
cookies are tasted in random order. Here are her results:
9. Use Scenario 11-4. The brand category that contributes the largest component to the 2 statistic is
A. B.
B. A.
C. C.
D. D.
E. All four components are roughly equal.
Cookie Brand
A
B
C
D
Total
Males
4
6
13
15
38
Females
22
12
11
13
58
Total
26
18
24
28
96
Ida wants to know if males and females prefer different brands of ready-made chocolate-chip cookie dough. She bakes eight dozen cookies from
dough made by each of four manufacturers which she labels brands A, B, C, and D. She then selects a simple random sample of 96 students, records
their gender, gives them one cookie of each brand and asks which brand they like best. Here are her results:
Scenario 11-5
10. Use Scenario 11-5. The conditional distribution for preferred cookie brand among males (in percents) is given by which of the following?
A. A: 4%; B: 6%; C: 13%; D: 15%
B. A: 27%; B: 19%; C: 25%; D: 29%
C. A: 11%; B: 16%; C: 34%; D: 39%
D. A: 23%; B: 13%; C: 11%; D: 14%
E. A: 38%; B: 21%; C: 19%; D: 22%
11. Use Scenario 11-5. If we want to compare the conditional distributions for preferred cookie brand among males to the same distribution for
females, which of the following is an appropriate graph to use?
A. Segmented bar graphs B. Scatterplot C. Parallel dotplots D. Side-by-side histograms E. Back-to-back stemplots
Scenario 11-10 A random sample of 200 Canadian students were asked about their hand dominance and whether they suffer from allergies. Here are
the results:
Allergies?
Yes
No
Ambidextrous
12
7
Hand
Left-handed
11
9
dominance
Right-handed
95
66
12. Use Scenario 11-10. Which of the following are appropriate null and alternative hypotheses for these data?
A. Ho: The distribution of hand dominance is the same for people with allergies and people without allergies.
H–a: Hand dominance and allergies are independent.
B. Ho: There is no association between hand dominance and allergies.
H–a: There is an association between hand dominance and allergies.
C. Ho: There is an association between hand dominance and allergies.
H–a: There is no association between hand dominance and allergies.
D. Ho: The distribution of hand dominance is different for people with allergies and people without allergies.
H–a: The distribution of hand dominance is the same for people with allergies and people without allergies.
E. Ho: Hand dominance and allergies are not independent.
H–a: Hand dominance and allergies are independent.
Scenario 11-1 Do certain car colors attract the attention of police more than others, so that they are more likely to get speeding tickets? A few years
ago a curious newspaper columnist tabulated the car color on a random sample of 120 speeding citations at the local courthouse. Here are his results.
Color
Red
White/Silver
Gray/Black
Other
Number of speeding tickets
16
33
39
32
He then went to the state motor vehicle registry and obtained data on the distribution of car colors for all cars registered in his state:
Color
Red
White/Silver
Gray/Black
Other
Percentage of cars on highway
14%
35%
23%
28%
13. Use Scenario 11-1. To answer the question posed above about car color and speeding tickets, the appropriate null hypothesis is:
A. The observed counts are all equal to 30. B. The observed counts are equal to the expected counts. C. The observed number of speeding tickets is
the same for all four color groups. D. The distribution of car colors for the speeding citations is the same as the distribution of colors for cars on the
highway. E. At least one of the four car color percentages is different from the other three.
14. Use Scenario 11-1. Which of the following are the correct expected counts for speeding tickets under the null hypothesis?
A.
B.
C.
D.
E.
15. Which of the following is a condition that must be satisfied to use a chi-square goodness-of-fit test?
A. The number of categories is small relative to the number of observations. B. The expected count for each category is greater than 5. C. The
population distribution is approximately Normal. D. The sample size is greater than 30. E. The expected count is the same for each category.
Scenario 11-11 Random samples of male and female high school students were asked to identify their favorite food group. Here are the results:
Gender
Female
Male
Carbohydrates
45
21
20
17
Favorite Food Dairy
Group
Fruits and vegetables
14
9
Proteins
7
17
Expected counts for each cell are given in the following table:
Gender
Favorite Food
Group
Carbohydrates
Dairy
Fruits and vegetables
Proteins
Female
37.8
21.2
13.2
13.8
Male
28.2
15.8
9.8
10.2
16. Use Scenario 11-11. Which of the following are appropriate null and alternative hypotheses for these data?
A. Ho: Favorite food group and gender are not independent.
Ha: Favorite food group and gender are independent.
B. Ho: The distribution of favorite food group is not the same for the two genders.
Ha: The distribution of favorite food group is the same for the two genders.
C.
D.
E.
Ho:
Ha:
Ho:
Ha:
Ho:
Ha:
The distribution of favorite food group is the same for both genders.
The distribution of favorite food group is not the same for both genders.
favorite food group and gender are independent.
There is no association between favorite food group and gender.
The distribution of gender is the same for all four food groups.
The distribution of gender is different for at least one food group.
17. Use Scenario 11-11. Which of the following cells contributions the most to the chi-square statistic?
A. Female/Carbohydrate B. Female/Proteins C. Female/Fruits and Vegetables D. Male/Proteins E. Male/Dairy
18.
A.
Use Scenario 11-11. Which of the following represents the individual component of chi-square contributed by the cell Female/Dairy?
B.
C.
D.
E.
Scenario 11-6 Are avid readers more likely to wear glasses than those who read less frequently? Three hundred men in the Korean army were
selected at random and classified according to whether or not they wore glasses and whether the amount of reading they did was above average,
average, or below average. The results are presented in the following table.
Wear Glasses?
Yes
No
Above Average
47
26
Amount of
Average
48
78
Reading
Below Average
31
70
Suppose we are testing the hypothesis that the amount or reading and wearing of glasses are independent.
19. Use Scenario 11-6. Suppose we wished to display in a graph the proportion of all above-average readers who wear glasses and do not wear
glasses, respectively. Which of the following graphical displays is best suited to this purpose?
A. A scatterplot B. A bar graph C. A boxplot D. A stemplot E. side-by-side histograms
20. Use Scenario 11-6. Suppose we wish to test the null hypothesis that there is no association between the amount of reading you do and whether
or not you wear glasses. Under the null hypothesis, which of the following is the expected number (approximately) of above-average readers who
wear glasses?
A. 27.2 B. 47 C. 19.7 D. 81.1 E. 30.7
Scenario 11-3 An ambitious reporter for a large university newspaper suspects that Mr. Hazzard, a new statistics teacher, is grading his introductory
statistics students too harshly. From school records the reporter determines that over the past 2 years the proportions of students in all sections of
introductory statistics (taught by many different teachers) received grades of A, B, C, D, or F in the following proportions: A: 0.20; B: 0.30; C: 0.30;
D: 0.10; and F: 0.10. The reporter then takes an SRS of 90 students who took introductory statistics with Mr. Hazzard in the past 2 years and gathers
the following information:
Grade
A
B
C
D
F
Number of students
12
26
28
15
9
The reporter performs the appropriate 2 procedure to test the hypothesis that the teacher’s grade distribution is different from other teachers of
introductory statistics.
21. Use Scenario 11-3. Which of the following conditions must be met before the reporter can use the 2 procedure in this situation??
A. The number of categories is small relative to the number of observations. B. The distribution of grades in all introductory statistics courses must
be approximately Normal. C. All the observed counts are greater than 5. D. All expected counts are approximately equal. E. Each observation
was randomly selected from the population of all grades given by the new teacher.
22. Use Scenario 11-3. The computed value of the 2 statistic for the reporter’s test is 6.074, which produces a P-value of 0.1937. Which of the
following is an appropriate conclusion?
A. Reject H0: there is convincing evidence from the test that the grade distribution of the new teacher is different from that of other teachers. B. Fail
to reject Ha: there is convincing evidence from the test that grade distribution of the new teacher is less harsh than that of other teachers. C. Accept
H0: there is convincing evidence from the test that the grade distribution of the new teacher is different from that of other teachers. D. Accept Ha:
there is convincing evidence from the test that grade distribution of the new teacher is harsher than that of other teachers. E. Fail to reject H0: there
is insufficient evidence from the test to conclude that the grade distribution of the new teacher is different from that of other teachers.
23.
A.
Which of the following statements is not true about chi-square distributions?
is larger for a chi-square distribution with df = 10 than for df = 1. B. They are always skewed right. C. The mean decreases as
the degrees of freedom increase. D. There are an infinite number of chi-square distributions, depending on degrees of freedom.
E.
24. Which of the following statements is true of chi-square distributions?
A. They take on only positive values. B. Their density curves are skewed to the left. C. As the number of degrees of freedom increases, their
density curves look more and more like a uniform distribution. D. As the number of degrees of freedom increases, their density curves look less and
less like a normal curve. E. All of the above are true.
Inference Review 3 - Chapter 11
Answer Section
MULTIPLE CHOICE
1.
ANS:
A
PTS:
1
TOP:
Components of chi-square in 2-way table
2.
ANS:
E
PTS:
1
TOP:
Conditions for chi-square procedures
3.
ANS:
E
PTS:
1
TOP:
Find P-value given chi-square statistic
4.
ANS:
A
PTS:
1
TOP:
Degrees of freedom for chi-sq 2-way table
5.
ANS:
B
PTS:
1
TOP:
Conclusion given chi-sq statistic and P-value
6.
ANS:
D
PTS:
1
TOP:
Find P-value given chi-square statistic
7.
ANS:
E
PTS:
1
TOP:
Degrees of freedom for chi-sq goodness-of-fit
8.
ANS:
B
PTS:
1
TOP:
Conditions for chi-square procedures
9.
ANS:
A
PTS:
1
TOP:
Component of chi-square statistic (comparing)
10.
ANS:
C
PTS:
1
TOP:
Conditional distribution from 2-way table
11.
ANS:
D
PTS:
1
TOP:
Graphical presentation of conditional distributions
12.
ANS:
B
PTS:
1
TOP:
Hypothesis for chi-square test of association
13.
ANS:
D
PTS:
1
TOP:
Null hypothesis for chi-square goodness-of-fit
14.
ANS:
A
PTS:
1
TOP:
Expected counts for chi-square goodness-of-fit
15.
ANS:
B
PTS:
1
TOP:
Conditions for chi-square procedures
16.
ANS:
C
PTS:
1
TOP:
Hypothesis for chi-square test of homogeneity
17.
ANS:
D
PTS:
1
TOP:
Components of chi-square in 2-way table
18.
ANS:
B
PTS:
1
TOP:
Components of chi-square in 2-way table
19.
ANS:
B
PTS:
1
TOP:
Graphical presentation of conditional distributors
20.
ANS:
E
PTS:
1
TOP:
Expected counts for chi-square 2-way table
21.
ANS:
E
PTS:
1
TOP:
Conditions for chi-square procedures
22.
ANS:
E
PTS:
1
TOP:
Conclusion given chi-sq statistic and P-value
23.
ANS:
C
PTS:
1
TOP:
Characteristics of chi-square distributions
24.
ANS:
A
PTS:
1
TOP:
Characteristics of chi-square distributions