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4th Edition

HEALEY + 1 other

Publisher: Cengage Learning,

ISBN: 9781305093836

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.

**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.

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.

**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

**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.

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.

**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

**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.

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