Multiple Choice Identify the
choice that best completes the statement or answers the question.
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1.
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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?
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2.
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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. |
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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 | | | | | | |
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3.
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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. |
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4.
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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 |
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5.
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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 |
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6.
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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. |
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7.
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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. |
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8.
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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). |
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9.
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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. |
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10.
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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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