# (a) To find: The column percentages and maximum difference.

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter 11, Problem 11.1P
To determine

## (a)To find:The column percentages and maximum difference.

Expert Solution

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,

1227×100=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,

44.4435=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,

6555.56=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.

Expert Solution

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,

620×100=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,

48.1530=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,

7051.85=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.

Expert Solution

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,

1533×100=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,

45.4528.57=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,

71.4354.55=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.

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