Question 1:
A survey was conducted to investigate the severity of rodent problems in egg and poultry operations. A random sample of operators was selected, and the operators were classified according to the type of operation and the extent of the rodent population. A total of 78 egg operators and 53 turkey operators were classified and the summary information is:
One reviewer of the study suggested that there may be a problem with the study because results from small operators were pooled with the results from large operators. Which of the following is NOT CORRECT?
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Simpson's paradox occurs when conclusions from a pooled table differ from the individual tables. |
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Tables can be pooled when the underlying rates are equal among tables. |
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Simpson's paradox occurs when tables with unequal row totals are pooled. |
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Inspection of the row or column percents will give a good clue if Simpson's paradox is likely to occur. |
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Simpson's paradox occurs when the pooled table gives no evidence of an effect but the individual tables show evidence of an effect. |
Question 2:
A survey was conducted to investigate the severity of rodent problems in egg and poultry operations. A random sample of operators was selected, and the operators were classified according to the type of operation and the extent of the rodent population. A total of 78 egg operators and 53 turkey operators were classified and the summary information is:
Which of the following is not correct?
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Operators who had both operations could not be used because this type of analysis requires each unit to be counted in one and only one cell. |
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The null hypothesis is that the severity of the rodent problem is independent of the type of operator. |
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The alternate hypothesis is that the proportion of turkey operators with mild, moderate, and severe rodent problems is different from the proportion of egg operators with mild, moderate, and severe rodent problems. |
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A Type I error would be to conclude that the severity of rodent problems is dependent upon the type of operator while, in fact, the proportion of turkey operators with mild, moderate, and severe rodent problems is the same as the proportion of egg operators with mild, moderate, and severe rodent problems. |
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A Type II error would be to conclude that the proportion of egg operators with mild, moderate, or severe rodent problems is the same as the proportion of turkey operators with mild, moderate, or severe rodent problems when in fact they are independent. |
Question 3:
In the paper "Color Association of Male and Female Fourth-Grade School Children" (J. Psych., 1988, 383-8), 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.
Frequency|
Row Pct | anger | happy | love | pain | Total
---------+--------+--------+--------+--------+---------+--------+--------+--------+
f | 27 | 19 | 39 | 17 | 102
| 26.47 | 18.63 | 38.24 | 16.67 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
m | 34 | 12 | 38 | 28 | 112
| 30.36 | 10.71 | 33.93 | 25.00 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
Total 61 31 77 45 214
Statistic DF Value Prob
-----------------------------------------------------------
Pearson Chi-Square * 4.629 *****
Likelihood Ratio Chi-Square * 4.661 *****
Mantel-Haenszel Chi-Square 1 0.307 *****
Under a suitable null hypothesis, the expected frequency for the cell corresponding to Anger and Males is:
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15.9 |
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55.7 |
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30.4 |
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31.9 |
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29.1 |
Question 4:
In the paper "Color Association of Male and Female Fourth-Grade School Children" (J. Psych., 1988, 383-8), 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.
Frequency|
Row Pct | anger | happy | love | pain | Total
---------+--------+--------+--------+--------+---------+--------+--------+--------+
f | 27 | 19 | 39 | 17 | 102
| 26.47 | 18.63 | 38.24 | 16.67 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
m | 34 | 12 | 38 | 28 | 112
| 30.36 | 10.71 | 33.93 | 25.00 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
Total 61 31 77 45 214
Statistic DF Value Prob
-----------------------------------------------------------
Pearson Chi-Square * 4.629 *****
Likelihood Ratio Chi-Square * 4.661 *****
Mantel-Haenszel Chi-Square 1 0.307 *****
The null hypothesis is:
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emotional association with red is independent of gender |
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gender is dependent upon the emotional association with red |
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the probability of selecting an emotion with red is related to gender |
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the number of children in each cell does not depend upon gender nor upon emotion |
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the color red is independent of the emotion associated with it and with gender. |
Question 5:
In the paper "Color Association of Male and Female Fourth-Grade School Children" (J. Psych., 1988, 383-8), 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.
Frequency|
Row Pct | anger | happy | love | pain | Total
---------+--------+--------+--------+--------+---------+--------+--------+--------+
f | 27 | 19 | 39 | 17 | 102
| 26.47 | 18.63 | 38.24 | 16.67 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
m | 34 | 12 | 38 | 28 | 112
| 30.36 | 10.71 | 33.93 | 25.00 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
Total 61 31 77 45 214
Statistic DF Value Prob
-----------------------------------------------------------
Pearson Chi-Square * 4.629 *****
Likelihood Ratio Chi-Square * 4.661 *****
Mantel-Haenszel Chi-Square 1 0.307 *****
Which of the following is not correct?
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A lower percentage of female students associate the emotion "anger" with the color red than do male students. |
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More students associate the color red with the emotion "love" than with the emotion "anger". |
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Each student was classified by gender and by emotion association. Each student was counted in one and only one cell. |
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We will be unable to compute a correlation for this data because the variables are not both interval or ratio in scale. |
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We compute row or column percentages by dividing the cell count by the table total (214). |
Question 6:
In the paper "Color Association of Male and Female Fourth-Grade School Children" (J. Psych., 1988, 383-8), 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.
Frequency|
Row Pct | anger | happy | love | pain | Total
---------+--------+--------+--------+--------+---------+--------+--------+--------+
f | 27 | 19 | 39 | 17 | 102
| 26.47 | 18.63 | 38.24 | 16.67 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
m | 34 | 12 | 38 | 28 | 112
| 30.36 | 10.71 | 33.93 | 25.00 |
---------+--------+--------+--------+--------+---------+--------+--------+--------+
Total 61 31 77 45 214
Statistic DF Value Prob
-----------------------------------------------------------
Pearson Chi-Square * 4.629 *****
Likelihood Ratio Chi-Square * 4.661 *****
Mantel-Haenszel Chi-Square 1 0.307 *****
The approximate p-value is:
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Between .100 and .900 |
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Between .050 and .100 |
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Between .025 and .050 |
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Between .010 and .025 |
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Between .005 and .010 |
(1): Simpson's paradox occurs when tables with unequal row totals are pooled.
(2): A Type II error would be to conclude that the proportion of egg operators with mild, moderate, or severe rodent problems is the same as the proportion of turkey operators with mild, moderate, or severe rodent problems when in fact they are independent
(3): 31.9
(4): emotional association with red is independent of gender.
(5): We compute row or column percentages by dividing the cell count by the table total (214).
(6): Between .100 and .900.
Question 1: A survey was conducted to investigate the severity of rodent problems in egg and...