analysis of two-way tables moore ips chapter 9 © 2012 w.h. freeman and company
TRANSCRIPT
Analysis of Two-Way Tables
Moore IPS Chapter 9
© 2012 W.H. Freeman and Company
A table has 4 rows and 5 columns. The degrees of freedom for a
test are
a. 10
b. 12
c. 20
9.1-1
9.1 Inference for Two-Way Tables
2
(r - 1)(c - 1) = 3 * 4 = 12
In the table below we examine the relationship between final grade and
the reported hours per week each student said they studied for the
course.
The size of this table is:
a. 4 x 6
b. 5 x 3
c. 3 x 5
9.1-2
9.1 Inference for Two-Way Tables
We are interested in comparing the proportions of males and females
who feel earning a large salary is very important to them. I surveyed
200 of each gender and recorded their answers to the question as “yes”
or “no.” If I analyze the data with both a z test for two proportions and a
test of no association, the P-value for the z test:
a. will be less than for the test.
b. will be the same as for the test.
c. will be more than for the test.
9.1-3
The data can be considered as either two proportions or a 2 by 2 table. The two are equivalent.
9.1 Inference for Two-Way Tables
2
22
2
A study to compare two types of infant formula was run at two sites,
Atlanta and Denver. Subjects at both sites were classified as dropouts if
they left the study before the conclusion, or completers if they finished
the study. The following table gives the number of dropouts and
completers at each site. A chi-square test was performed and the result
was 2 = 5.101 with P-value = 0.024.
The correct conclusion is:
a. Atlanta had a greater dropout rate.
b. Denver had a greater dropout rate.
c. any differences can be explained by sampling variability.
9.1-4
9.1 Inference for Two-Way Tables
Responder
Dropout Completer
Atlanta 16 134
Denver 21 379
In a clinical trial of Nasonex, 200 randomly selected pediatric patients (ages 3 to 11 years old) were randomly divided into two groups. The patients in Group 1 (experimental group) received 100 mcg of Nasonex, while the patients in Group 2 (control group) received a placebo. Of the 100 patients in the experimental group, 30 reported headaches as a side effect. Of the 100 patients in the control group, 80 reported headaches as a side effect.
Which of the following could be used to test the hypothesis Ho: p1 = p2 versus Ha: p1 ≠ p2 ?
a. t2 = F
b. z2 = F
c. χ2 = F
d. t2 = χ2
e. z2 = χ2
9.1-5
9.1 Inference for Two-Way Tables
In the table below we examine the relationship between final grade and
the reported hours per week each student said they studied for the
course.
The expected count of those who studied between 5 and 10 hours per
week and earned a B for the course is:
a. 4.672
b. 4.266
c. 8.265
9.2-1
9.1 Inference for Two-Way Tables
13 234.671875
64
When examining the independence of two-way tables using the chi-square test, the null hypothesis is:
a. that the row and column variables are dependent.
b. that the row and column variables are independent.
c. that the row and column variables are equal.
9.2-2
9.2 Formulas and Models for Two-Way Tables
The Ecology department head is examining the course evaluations for four different sections of an introductory course taught by different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Below are the results:
9.2-3 (part 1)
9.2 Formulas and Models for Two-Way Tables
What is the null hypothesis being tested in this case?
a. Opinions of students are homogenous with respect to the quality of teaching they received.
b. Opinions of students are independent with respect to the quality of teaching they received.
c. Opinions of students are not associated with respect to the quality of teaching they received.
9.2 Formulas and Models for Two-Way Tables
9.2-3 (part 2)
The Ecology department head is examining the course evaluations for four different sections of an introductory course taught by different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Below are the results:
9.2-4 (part 1)
9.2 Formulas and Models for Two-Way Tables
What is the expected count of positive ratings for the instructor from section A01?
a. 25.17
b. 35.17
c. 15.17
9.2 Formulas and Models for Two-Way Tables
9.2-4 (part 2)
E (62)(34)
139
The Ecology department head is examining the course evaluations for four different sections of an introductory course taught by different instructors. He would like to know if the opinions of students are homogeneous with respect to the quality of instruction they received from their respective professors. Below are the results:
9.2-5 (part 1)
9.2 Formulas and Models for Two-Way Tables
What is the degree of freedom for the appropriate test statistic for the above problem?
a. 6
b. 8
c. 12
9.2 Formulas and Models for Two-Way Tables
9.2-5 (part 2)
df = (r-1)(c-1)= 2(3) = 6
In the table below we examine the relationship between final grade and
the reported hours per week each student said they studied for the
course.
In a test of no association between these variables, we are really
studying a model of:
a. independence.
b. comparing several populations.
c. neither a nor b.
9.2-6
9.2 Formulas and Models for Two-Way Tables
The table below is referred to as a
a. 3 x 6 table.
b. 3 x 5 table.
c. 2 x 5 table.
d. 5 x 2 table.
e. 5 x 3 table.
9.2-7
9.3 Goodness of Fit
GenderMale Female
Like Very Much 16 14
Like Somewhat 13 18
Neutral 17 16
Dislike Somewhat 3 2
Dislike Very Much 1 0
Two-way tables are classified as r x c.
A die is tossed 60 times and the number of dots appearing on the top
face are recorded in the table below.
An investigator wants to know if there is enough evidence to indicate that
the die is not fair. What is the most appropriate test?
a. Chi-square: Independence test
b. Chi-square: Comparing several proportions test
c. Chi-square: Goodness of fit test
9.3-1
.
9.3 Goodness of Fit
Top Face 1 2 3 4 5 6
# of occurrences 8 12 13 9 11 7
A die is tossed 60 times and the number of dots appearing on the top
face are recorded in the table below.
An investigator wants to know if there is enough evidence to indicate that
the die is not fair.
What is the expected number of 3s if the die is fair?
a. 6
b. 7
c. 10
d. 11
.
9.3 Goodness of Fit
Top Face 1 2 3 4 5 6
# of occurrences 8 12 13 9 11 7
9.3-2
1/6 * 60
A die is tossed 60 times and the number of dots appearing on the top
face are recorded in the table below.
An investigator wants to know if there is enough evidence to indicate that
the die is not fair.
What are the appropriate degrees of freedom for the chi-square test?
a. 5
b. 6
c. 10
d. 12
.
9.3 Goodness of Fit
Top Face 1 2 3 4 5 6
# of occurrences 8 12 13 9 11 7
1 6 1 5k
9.3-3
A die is tossed 60 times and the number of dots appearing on the top
face are recorded in the table below.
An investigator wants to know if there is enough evidence to indicate that
the die is not fair.
The value of the chi-square statistic is 2.8. Is there sufficient evidence to
conclude that the die is not fair? Use = 0.05.
a. Yes
b. No
.
9.3 Goodness of Fit
Top Face 1 2 3 4 5 6
# of occurrences 8 12 13 9 11 7
9.3-4
11.07
.7308
Critical value
p value
A die is tossed 60 times and the number of dots appearing on the top
face are recorded in the table below.
An investigator wants to know if there is enough evidence to indicate that
the die is not fair.
Using the output provided, is there sufficient evidence to conclude that the
die is not fair? Use = 0.05.
a. Yes
b. No
.
9.3 Goodness of Fit
Top Face 1 2 3 4 5 6
# of occurrences 8 12 13 9 11 7
9.3-4c
C
It is desired to test whether the number of gamma rays emitted per second by a certain radioactive substance is a Poisson random variable. The following data give the results obtained from 150 one-second intervals. The mean was estimated from the data as 2.8 gamma rays per second. Some expected frequencies are given.
# of Ga Rays: 0 1 2 3 4 5 6 7
Obs Count: 10 25 32 37 21 16 7 2
Exp freq: 9.1 25.5 13.1 6.1 2.4
The degrees of freedom for the appropriate test statistic is:
a. 4
b. 5
c. 6
d. 7
.
9.3 Goodness of Fit
9.3-5
k-1-# of parameters estimated = 7-1-1 = 5