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G E R A survey of senior citizens who live in either a housing development specifically designed for retirees or an age-integrated neighborhood has been conducted. Is type of living arrangement related to sense of social isolation? Analyze the relationship with column percentages, the maximum difference, and an appropriate measure of association. Summarize your findings in a paragraph. Sense of Isolation Living Arrangement Housing Development Integrated Neighborhood Totals Low 80 30 110 High Totals 20 100 120 150 140 250

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Essentials Of Statistics

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

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Chapter
Section
BuyFindarrow_forward

Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 11, Problem 11.3P
Textbook Problem
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G E R A survey of senior citizens who live in either a housing development specifically designed for retirees or an age-integrated neighborhood has been conducted. Is type of living arrangement related to sense of social isolation? Analyze the relationship with column percentages, the maximum difference, and an appropriate measure of association. Summarize your findings in a paragraph.

Sense of Isolation Living Arrangement
Housing Development Integrated Neighborhood Totals
Low 80 30 110
High
Totals
20 100 120 150 140 250

To determine

To find:

The column percentages, strength and pattern of relationship.

Explanation of Solution

Given:

The given statement is,

A survey of senior citizens who live in either a housing development specifically designed for retirees or an age-integrated neighborhood has been conducted.

The given table of information is,

Sense of isolation Living arrangement
Housing Development Integrated Neighborhood Totals
Low 80 30 110
High 20 120 140
Totals 100 150 250

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.

If the gamma value is less than 0.30, it is said that there is a weak association between the categories.

If the gamma value is greater than 0.60, it is said that there is a strong association between the categories.

The gamma compares the number of pairs of cases ranked in the same order on both variables (Ns) with the number of cases ranked in different order (Nd).

Formula used:

For compares the number of pairs of cases ranked in the same order on both variables (Ns) with the number of cases ranked in different order (Nd) the gamma G is given as,

G=NsNdNs+Nd

Calculation:

From the given table of information,

The value of Ns is computed as,

Ns=80×120=9600

And the value of Nd is computed as,

Nd=20×30=600

The gamma value is given by,

G=NsNdNs+Nd

Substitute 9600 for Ns and 600 for Nd in the above formula

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