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S O C A small sample of non-English-speaking immigrants to the United States has been interviewed about their level of assimilation. Is the pattern of adjustment affected by length of residence in the United States? For each table compute gamma and summarize the relationship in terms of strength and direction. a. English fluency Length of Residence English Fluency Less than Five Years (Low) More than five Years (High) Totals Low 20 10 30 High 5 _ 15 _ 20 _ Totals 25 20 50 b. Total family income Length of Residence Income Less than Five Years (Low) More than five Years (High) Totals Low 18 8 26 High 7 _ 17 _ 24 _ Totals 25 25 50 c. Extent of contact with country of origin Length of Residence Contact Less than Five Years (Low) More than five Years (High) Totals Rare 5 20 25 Frequent 20 _ 5 _ 25 _ Totals 25 25 50

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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 11.6P
Textbook Problem
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S O C A small sample of non-English-speaking immigrants to the United States has been interviewed about their level of assimilation. Is the pattern of adjustment affected by length of residence in the United States? For each table compute gamma and summarize the relationship in terms of strength and direction.

a. English fluency

Length of Residence
English Fluency Less than Five Years (Low) More than five Years (High) Totals
Low 20 10 30
High    5 _   15 _   20 _
Totals 25 20 50

b. Total family income

Length of Residence
Income Less than Five Years (Low) More than five Years (High) Totals
Low 18 8 26
High   7 _   17 _   24 _
Totals 25 25 50

c. Extent of contact with country of origin

Length of Residence
Contact Less than Five Years (Low) More than five Years (High) Totals
Rare 5 20 25
Frequent   20 _   5 _   25 _
Totals 25 25 50

To determine

(a)

To find:

The gamma and the relationship in terms of strength and direction.

Explanation of Solution

Given:

A small sample of non-English-speaking immigrants to the United States has been interviewed about their level of assimilation.

The given table of information is,

Length of Residence
English Fluency Less than Five Years (Low) More than five Years (High) Totals
Low 20 10 30
High 5 15 20
Totals 25 20 50

Approach:

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:

To compare 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=20×15=300

And the value of Nd is computed as,

To determine

(b)

To find:

The gamma and the relationship in terms of strength and direction.

To determine

(c)

To find:

The gamma and the relationship in terms of strength and direction.

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