# S O C At a large urban college, about half of the students live off campus in various arrangements, and the other half live on campus. Is academic performance dependent on living arrangements? Write a sentence or two explaining your findings, including the results of the chi square test and pattern of column percentages. GPA Residential Status Off Campus with Roommates Off Campus with Parents On Campus Totals Low 22 20 48 90 Moderate 36 40 54 130 High Totals 32 90 10 70 38 140 80 300

### Essentials Of Statistics

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

Chapter
Section

### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836
Chapter 10, Problem 10.11P
Textbook Problem
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## S O C At a large urban college, about half of the students live off campus in various arrangements, and the other half live on campus. Is academic performance dependent on living arrangements? Write a sentence or two explaining your findings, including the results of the chi square test and pattern of column percentages. GPA Residential Status Off Campus with Roommates Off Campus with Parents On Campus Totals Low 22 20 48 90 Moderate 36 40 54 130 HighTotals 32 90 10 70 38 140 80 300

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,

 GPA Residential Status Off Campus with Roommates Off Campus with Parents On Campus Totals Low 22 20 48 90 Moderate 36 40 54 130 High 32 10 38 80 Totals 90 70 140 300

Approach:

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 90 for row marginal, 90 for column marginal and 300 for N in equation (1).

f1=90×90300=27

Substitute 90 for row marginal, 70 for column marginal and 300 for N in equation (1).

f2=90×70300=21

Substitute 90 for row marginal, 38 for column marginal and 300 for N in equation (1).

f3=90×140300=42

Substitute 130 for row marginal, 90 for column marginal and 300 for N in equation (1).

f4=130×90300=39

Substitute 130 for row marginal, 70 for column marginal and 300 for N in equation (1).

f5=130×70300=30.33

Substitute 130 for row marginal, 140 for column marginal and 300 for N in equation (1).

f6=130×140300=60.67

Substitute 80 for row marginal, 90 for column marginal and 300 for N in equation (1).

f7=80×90300=24

Substitute 80 for row marginal, 70 for column marginal and 300 for N in equation (1).

f8=80×70300=18.67

Substitute 80 for row marginal, 140 for column marginal and 300 for N in equation (1).

f9=80×140300=37.33

Consider the following table,

 fo fe fo−fe (fo−fe)2 (fo−fe)2/fe 22 27 −5 25 0

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