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AP Statistics - Chapter 11: The Chi-Square Distributions


Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 
A chi-square goodness of fit test is used to test whether a 0 to 9 spinner is “fair” (that is, the outcomes are all equally likely).  The spinner is spun 100 times, and the results are recorded.  What are the degrees of freedom for this test?
a.
8
b.
9
c.
10
d.
99
e.
100
 

 2. 
A study of accident records at a large engineering company in England reported the following number of injuries on each shift for 1 year:

                        Shift:   Morning         Afternoon     Night
            Number of injuries:      1372            1578            1686

Is there sufficient evidence to say that the numbers of accidents on the three shifts are not the same?  Test at the 0.05, 0.01, and 0.001 levels.
a.
There is sufficient evidence at all three levels to say that the numbers of accidents on each shift are not the same.
b.
There is sufficient evidence at the 0.05 and 0.01 levels but not at the 0.001 level.
c.
There is sufficient evidence at the 0.05 level but not at the 0.01 or 0.001 levels.
d.
There is sufficient evidence at the 0.001 level but not at the 0.01 or 0.05 levels.
e.
There is insufficient evidence at any of these levels.
 
 
Questions 3 to 10 refer to the following situation.
In the paper “Color Association of Male and Female Fourth-Grade School Children” (Journal of Psychology, 1988, 383–388), reported on a study in which children were asked to indicate what emotion they associated with the color red. The response and the sex of the child are noted and summarized below. The first number in each cell is the count; the second number is the row percent.

 
Anger
Happy
Love
Pain
Total
Female
27
26.47
19
18.63
39
38.24
17
16.67
102
Male
34
30.36
12
10.71
38
33.93
28
25.00
112
Total
61
31
77
45
214
 

 3. 
The null hypothesis is
a.
emotional association with red is independent of gender.
b.
gender is dependent upon the emotional association with red.
c.
the probability of associating a specific emotion with red is related to gender.
d.
the number of children in each cell does not depend upon gender or upon emotion.
e.
the color red is independent of the emotion associated with it and with gender.
 

 4. 
Under a suitable null hypothesis, the expected frequency for the cell corresponding to Anger and Males is
a.
15.9
b.
55.7
c.
30.4
d.
31.9
e.
29.1
 

 5. 
The null hypothesis will be rejected at a = 0.05 if the test statistic exceeds
a.
3.84
b.
5.99
c.
7.81
d.
9.49
e.
14.07
 

 6. 
The approximate P-value is
a.
between 0.100 and 0.900.
b.
between 0.050 and 0.100.
c.
between 0.025 and 0.050.
d.
between 0.010 and 0.025.
e.
between 0.005 and 0.010.
 

 7. 
Which of the following is NOT CORRECT?
a.
The children were classified by sex and emotion associated with red. Each child was counted in one and only one cell.
b.
The null hypothesis is that the type of emotion associated with red is independent of the sex of the child.
c.
The null hypothesis is that the proportion of emotions associated with red is the same for both sexes.
d.
All expected cell counts should be greater than 5 in order that the distribution of the test statistic is an approximate chi-square distribution.
e.
If we reject the null hypothesis, then we have proven that the two sexes associate red with emotions in different ways.
 

 8. 
Which of the following is NOT CORRECT?
a.
A lower percent of female students associate the emotion “anger” with the color red than do male students.
b.
More students associate the color red with the emotion “love” than with the emotion “anger.”
c.
There is insufficient evidence of an association between gender and emotion associated with the color red.
d.
We will be unable to compute a correlation for these data because the variables are both categorical.
e.
We compute row or column percents by dividing the cell count by the table total (214).
 

 9. 
A Type I error would be committed if
a.
we conclude that the sex of the child and the emotion associated with red are independent when in fact they are not independent.
b.
we conclude that the sex of the child and the emotion associated with red are not independent when in fact they are not independent.
c.
we conclude that the proportion of emotions associated with red differs between males and females when in fact they are the same.
d.
we conclude that the proportion of emotions associated with red is the same for males and females when in fact they are the same.
e.
we fail to find any association between the color red and emotions for either sex.
 

 10. 
The test statistic and approximate P-value are
a.
4.661       0.1983
b.
4.661       0.3966
c.
4.629       0.2011
d.
4.629       0.4022
e.
4.629       0.1006
 



 
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