Chapter 11, Problem 11.1P

$\boxed{SOC}$ 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. Is there any association between support for raising fees and the gender, discipline, or tenured status of the faculty? Use column percentages, the maximum difference, and an appropriate measure of association to describe the strength and pattern of these associations.

a. Support for raising fees by gender

Support?	Gender
	Males	Females	Totals
For	12	7	19
Against Totals	$\frac{15}{27}$	$\frac{13}{20}$	$\frac{28}{47}$

b. Support for raising fees by discipline

Support?	Discipline
	Liberal Arts	Science and Business	Totals
For	6	13	19
Against Totals	$\frac{14}{20}$	$\frac{14}{27}$	$\frac{28}{47}$

c. Support for raising fees by tenured status

Support?	Status
	Tenured	Nontenured	Totals
For	15	4	19
Against Totals	$\frac{18}{33}$	$\frac{10}{14}$	$\frac{28}{47}$

To determine

(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,

$\frac{12}{27}\times 100=44.44\%$

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,

$44.44-35=9.44\%$

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,

$65-55.56=9.44\%$

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.

To determine

(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,

$\frac{6}{20}\times 100=30\%$

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,

$48.15-30=18.15\%$

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,

$70-51.85=18.15\%$

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.

To determine

(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,

$\frac{15}{33}\times 100=45.45\%$

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,

$45.45-28.57=16.88\%$

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,

$71.43-54.55=16.88\%$

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.