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a. Support for raising fees by gender
| Support? | Gender | ||
| Males | Females | Totals | |
| For | 12 | 7 | 19 |
| Against Totals |
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b. Support for raising fees by discipline
| Support? | Discipline | ||
| Liberal Arts | Science and Business | Totals | |
| For | 6 | 13 | 19 |
| Against Totals |
|
|
|
c. Support for raising fees by tenured status
| Support? | Status | ||
| Tenured | Nontenured | Totals | |
| For | 15 | 4 | 19 |
| Against Totals |
|
|
|
(a)
To find:
The column percentages and maximum difference.
Answer to Problem 11.1P
Solution:
The column percentage table of the given data is,
| Support? | Gender | |
| Males | Females | |
| For | 44.44% | 35% |
| Against | 55.56% | 65% |
| Totals | 100% | 100% |
The maximum difference is 9.44%.
The strength of association is weak.
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
Explanation of Solution
Given:
The given statement is,
The administration of a local college campus wants to increase the mandatory student fee to finance an upgrading of the football program. A survey of a sample of faculty regarding this proposal has been completed.
The given table of information is,
| Support? | Gender | ||
| Males | Females | Totals | |
| For | 12 | 7 | 19 |
| Against | 15 | 13 | 38 |
| Totals | 27 | 20 | 47 |
Approach:
If the maximum difference of the smallest and the largest column percentage in a row is less than 10%, it is said that there is a weak association between the categories.
If the maximum difference is between 10% and 30%, it is said that there is a moderate association between the categories and if the maximum difference is above 30%, then there is a high association between the categories.
Calculation:
From the given information,
The following table gives the column wise percentages based on gender.
| Support? | Gender | |
| Males | Females | |
| For | 44.44% | 35% |
| Against | 55.56% | 65% |
| Totals | 100% | 100% |
The columns of the table are computed as,
Substitute the values from the given table of information,
Proceed in a similar manner to obtain rest of the values of the table.
For the first row,
The maximum percentage is 44.44%.
The minimum percentage is 35%.
The difference is given as,
The difference for the first row is 9.44%.
For the second row,
The maximum percentage is 65%.
The minimum percentage is 55.56%.
The difference is given as,
The difference for the second row is 9.44%.
The maximum difference is 9.44%.
Since, 9.44% is less than 10%, it shows that the strength of association is weak.
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
Conclusion:
The column percentage table of the given data is,
| Support? | Gender | |
| Males | Females | |
| For | 44.44% | 35% |
| Against | 55.56% | 65% |
| Totals | 100% | 100% |
The maximum difference is 9.44%.
The strength of association is weak.
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
(b)
To find:
The column percentages and maximum difference.
Answer to Problem 11.1P
Solution:
The column percentage table of the given data is,
| Support? | Discipline | |
| Liberal Arts | Science and Business | |
| For | 30% | 48.15% |
| Against | 70% | 51.85% |
| Totals | 100% | 100% |
The maximum difference is 18.15%.
The strength of association is moderate.
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
Explanation of Solution
Given:
The given statement is,
The administration of a local college campus wants to increase the mandatory student fee to finance an upgrading of the football program. A survey of a sample of faculty regarding this proposal has been completed.
The given table of information is,
| Support? | Discipline | ||
| Liberal Arts | Science and Business | Totals | |
| For | 6 | 13 | 19 |
| Against | 14 | 14 | 38 |
| Totals | 20 | 27 | 47 |
Approach:
If the maximum difference of the smallest and the largest column percentage in a row is less than 10%, it is said that there is a weak association between the categories.
If the maximum difference is between 10% and 30%, it is said that there is a moderate association between the categories and if the maximum difference is above 30%, then there is a high association between the categories.
Calculation:
From the given information,
The following table gives the column wise percentages based on discipline.
| Support? | Discipline | |
| Liberal Arts | Science and Business | |
| For | 30% | 48.15% |
| Against | 70% | 51.85% |
| Totals | 100% | 100% |
The columns of the table are computed as,
Substitute the values from the given table of information,
Proceed in a similar manner to obtain rest of the values of the table.
For the first row,
The maximum percentage is 48.15%.
The minimum percentage is 30%.
The difference is given as,
The difference for the first row is 18.15%.
For the second row,
The maximum percentage is 70%.
The minimum percentage is 51.85%.
The difference is given as,
The difference for the second row is 18.15%.
The maximum difference is 18.15%.
Since, 18.15% is between 10% and 30%, it shows that the strength of association is moderate
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
Conclusion:
The column percentage table of the given data is,
| Support? | Discipline | |
| Liberal Arts | Science and Business | |
| For | 30% | 48.15% |
| Against | 70% | 51.85% |
| Totals | 100% | 100% |
The maximum difference is 18.15%.
The strength of association is moderate.
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
(c)
To find:
The column percentages and maximum difference.
Answer to Problem 11.1P
Solution:
The column percentage table of the given data is,
| Support? | Discipline | |
| Tenured | Nontenured | |
| For | 45.45% | 28.57% |
| Against | 54.55% | 71.43% |
| Totals | 100% | 100% |
The maximum difference is 16.88%.
The strength of association is moderate.
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
Explanation of Solution
Given:
The given statement is,
The administration of a local college campus wants to increase the mandatory student fee to finance an upgrading of the football program. A survey of a sample of faculty regarding this proposal has been completed.
The given table of information is,
| Support? | Status | ||
| Tenured | Nontenured | Totals | |
| For | 15 | 4 | 19 |
| Against | 18 | 10 | 38 |
| Totals | 33 | 14 | 47 |
Approach:
If the maximum difference of the smallest and the largest column percentage in a row is less than 10%, it is said that there is a weak association between the categories.
If the maximum difference is between 10% and 30%, it is said that there is a moderate association between the categories and if the maximum difference is above 30%, then there is a high association between the categories.
Calculation:
From the given information,
The following table gives the column wise percentages based on tenured status.
| Support? | Status | |
| Tenured | Nontenured | |
| For | 45.45% | 28.57% |
| Against | 54.55% | 71.43% |
| Totals | 100% | 100% |
The columns of the table are computed as,
Substitute the values from the given table of information,
Proceed in a similar manner to obtain rest of the values of the table.
For the first row,
The maximum percentage is 45.45%.
The minimum percentage is 28.57%.
The difference is given as,
The difference for the first row is 16.88%.
For the second row,
The maximum percentage is 71.43%.
The minimum percentage is 54.55%.
The difference is given as,
The difference for the second row is 16.88%.
The maximum difference is 16.88%.
Since, 16.88% is between 10% and 30%, it shows that the strength of association is moderate
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
Conclusion:
The column percentage table of the given data is,
| Support? | Discipline | |
| Tenured | Nontenured | |
| For | 45.45% | 28.57% |
| Against | 54.55% | 71.43% |
| Totals | 100% | 100% |
The maximum difference is 16.88%.
The strength of association is moderate.
In the column table, high percentage of one variable is associated with low percentage of another variable, therefore there is a positive association between the variables.
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Chapter 11 Solutions
Essentials Of Statistics
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