   # S O C Is there a statistically significant relationship between length of marriage and satisfaction with marriage? The necessary information has been collected from a random sample of 100 respondents drawn from a local community. Write a sentence or two explaining your findings, including the results of the chi square test and pattern of column percentages. Satisfaction Length of Marriage (in years) Less than 5 5-10 More than 10 Totals Low 10 20 20 50 High Totals 20 30 20 40 10 30 50 100 ### Essentials Of Statistics

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

#### Solutions

Chapter
Section ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.9P
Textbook Problem
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## S O C Is there a statistically significant relationship between length of marriage and satisfaction with marriage? The necessary information has been collected from a random sample of 100 respondents drawn from a local community. Write a sentence or two explaining your findings, including the results of the chi square test and pattern of column percentages. Satisfaction Length of Marriage (in years) Less than 5 5-10 More than 10 Totals Low 10 20 20 50 HighTotals 20 30 20 40 10 30 50 100

To determine

To find:

The chi square value for the given information and test for its significance.

### Explanation of Solution

Given:

The given statement is,

The necessary information has been collected from a random sample of 100 respondents drawn from a local community.

The given table of information is,

 Satisfaction Length of Marriage (in years) Less than 5 5-10 More than 10 Totals Low 10 20 20 50 High 20 20 10 50 Totals 30 40 30 100

Concept:

The confidence interval is an interval estimate from the statistics of the observed data that might contain the true value of the unknown population parameter.

The five step model for hypothesis testing is,

Step 1. Making assumptions and meeting test requirements.

Step 2. Stating the null hypothesis.

Step 3. Selecting the sampling distribution and establishing the critical region.

Step 4. Computing test statistics.

Step 5. Making a decision and interpreting the results of the test.

Formula used:

For a chi square, the expected frequency fe is given as,

fe=Rowmarginal×ColumnmarginalN

Where N is the total of frequencies.

The chi square statistic is given by,

χ2(obtained)=(fofe)2fe

Where fo is the observed frequency,

And fe is the expected frequency.

The degrees of freedom for the bivariate table is given as,

df=(r1)(c1)

Where r is the number of rows and c is the number of columns.

Calculation:

From the given information,

The observed frequency is given as,

fe=Rowmarginal×ColumnmarginalN……(1)

Substitute 50 for row marginal, 30 for column marginal and 100 for N in equation (1).

f1=50×30100=15

Substitute 50 for row marginal, 40 for column marginal and 100 for N in equation (1).

f2=50×40100=20

Substitute 50 for row marginal, 30 for column marginal and 100 for N in equation (1).

f3=50×30100=15

Substitute 50 for row marginal, 30 for column marginal and 100 for N in equation (1).

f4=50×30100=15

Substitute 50 for row marginal, 40 for column marginal and 100 for N in equation (1).

f5=50×40100=20

Substitute 50 for row marginal, 30 for column marginal and 100 for N in equation (1).

f6=50×30100=15

Consider the following table,

 6.25 fo fe fo−fe (fo−fe)2 (fo−fe)2/fe 10 15 −5 25 1.67 20 20 0 0 0 20 15 5 25 1

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