Download Practice questions on categorical data techniques

STAT412
Analysis of Categorical Data
Practice Questions
1. 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?” A two-way table summarizing the results for 953 respondents, by gender,
is shown below:
Gender
Female
Male
Total
Yes
488
335
823
No
66
64
130
Total
554
399
953
If the null hypothesis were true, what is the expected number of women in the sample who would give a “No” response
to having a female president?
A)
B)
C)
D)
54.4
66.0
75.6
None of the above
2. About 90% of the general population are right-handed. A researcher speculates that artists are less likely to be righthanded than the general population. In a random sample of 100 artists, 83 are right-handed. Which of the following best
describes the p-value for this situation?
A) The probability that the population proportion of artists who are right-handed is 0.90.
B) The probability that the population proportion of artists who are right-handed is 0.83.
C) The probability the sample proportion would be as small as 0.83, or even smaller, if the population proportion of
artists who are right-handed is actually 0.90.
D) The probability that the population proportion of artists who are right-handed is less than 0.90, given that the sample
proportion is 0.83.
3. Suppose the present success rate in the treatment of a particular psychiatric disorder is 65%. A research group hopes
to demonstrate that the success rate of a new treatment will be better than this standard. Which of the following
describes a type 2 error for this problem?
A) Claiming that the success rate of the new treatment is greater than 65% when really it isn't.
B) Failing to decide that the success rate is greater than 65% when actually it is.
C) Using a one-sided alternative hypothesis when a two-sided alternative should have been used.
D) Using a two-sided alternative hypothesis when a one-sided alternative should have been used.
4. 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 degrees of freedom would
be used in conducting the hypothesis test?
A) 24
B) 20
C) 15
D) 5
5. Are the educational aspirations of students related to family income? This question was investigated in the article
“Aspirations and Expectations of High School Youth” (Int. J. of Comp. Soc. (1975): 25). The accompanying 4 X 3 table
resulted from classifying 273 students according to expected level of education and family income. Using =.05, the
appropriate rejection region would be: reject Ho if the test statistic value is
Income
Aspired Level
Low
Middle
High
Some High School
9
11
9
High School Graduate
44
52
41
Some College
13
23
12
College Graduate
10
22
27
A)
B)
C)
D)
 5.99
 12.59
 7.81
 21.03
6. An airport official wants to prove that the 1 = proportion of delayed flights after a storm for Airline 1 was different
from 2 = the proportion of delayed flights for Airline 2. Random samples from the two airlines after a storm showed
that 50 out of 100 (.50) of Airline A’s flights were delayed, and 70 out of 200 (.35) of Airline B’s flights were delayed.
What is the value of the test statistic?
A) 2.50
B) 2.00
C) 0.79
D) None of the above
7. In the 1994 General Social Survey, a nationwide survey done every other year in the United States, the 1,185
respondents who had ever been married were asked the age at which they first wed and whether they had ever been
divorced. The two-way table below summarizes the observed counts for the relationship between “age first wed”
(categorized into four age groups) and “ever divorce” (no or yes). A chi-square value and p-value are given below the
table.
Rows: Age First Wed
Under 20
20-24
25-29
30+
All
No
150
340
156
76
722
Columns: Ever Divorced
Yes
173
194
69
27
463
All
323
534
225
103
1185
Chi-Square = 44.00, DF = __ , P-Value = 0.000
The p-value is given as 0.000. This value was calculated as
A. The area to the right of 44.00 in a chi-square distribution with df = 3.
B. The area to the right of 44.00 in a chi-square distribution with df = 8
C. The area to the left of 44.00 in a chi-square distribution with df = 3
D. The area to the left of 44.00 in a chi-square distribution with df = 8
8. A medical researcher hypothesizes that, within a particular ethnic group, the distribution of blood types is: 50% have
type O, 25% have type A, 20% have type B, and 5% have type AB. He gathers blood type data for a random sample of
400 people from this ethnic group, and summarizes the observed counts in the following table.
Blood type
Count
O
185
A
106
B
85
AB
24
Total
400
Suppose that a chi-square goodness of fit test is performed, and the null hypothesis is the researcher’s hypothesis. What
are the expected counts for blood types O, A, B, and AB, respectively?
A. 100, 100, 100, 100
B. 185, 106, 85, 24
C. 200, 100, 80, 20
D. 50, 25, 20, 5
Questions 9 to 13: A gambler wanted to test whether or not a die was fair. He rolled the die 180 times and got the
results shown below. For example, the number “1” appeared on 40 rolls.
Die Result
Frequency
1
40
2
40
3
30
4
30
5
20
6
20
Total
180
9. What is the null hypothesis for this chi-square goodness of fit test?
A. The probability of a 1, 2, … 6 is 40/180, 40/180, …, 20/180, respectively.
B. The die is not fair: the probabilities of getting a particular number (like “1”) are not all equal.
C. The die is fair: the probability of getting any particular number (like “1”) is 1/6.
D. None of the above
10. What are the degrees of freedom for the chi-square goodness of fit statistic?
A. 6
B. 5
C. 4
D. None of the above
11. What is the value for the goodness of fit chi-square statistic?
A.
0.00
B.
6.50
C. 13.33
D. None of the above
12. What is the p-value range?
A. p < .005
B. .01 < p < .025
C. 05 < p < .075
D. None of the above
13. At a significance level of .05, what is your conclusion?
A. The null hypothesis is rejected: the die is not fair.
B. The null hypothesis is rejected: the die is fair.
C. The null hypothesis is not rejected: there is insufficient evidence to conclude the die is not fair.
D. The null hypothesis is not rejected: there is sufficient evidence to conclude the die is fair.