# P S Is there a relationship between college class standing and political orientation? Are juniors and seniors significantly different from freshmen and sophomores on this variable? The following table reports the relationship between these two variables for a random sample of 267 college students. Summarize your findings in a sentence or two, including the results of the chi square test and the pattern of column percentages. Which group is more likely to be liberal? Which group is more likely to be conservative? Political Views Class Standing Freshmen and Sophomore Junior and Senior Totals Liberal 40 43 83 Moderate 50 50 100 Conservative Totals 44 134 40 133 84 267

### 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 10.10P
Textbook Problem
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## P S Is there a relationship between college class standing and political orientation? Are juniors and seniors significantly different from freshmen and sophomores on this variable? The following table reports the relationship between these two variables for a random sample of 267 college students. Summarize your findings in a sentence or two, including the results of the chi square test and the pattern of column percentages. Which group is more likely to be liberal? Which group is more likely to be conservative? PoliticalViews Class Standing Freshmen and Sophomore Junior and Senior Totals Liberal 40 43 83 Moderate 50 50 100 ConservativeTotals 44 134 40 133 84 267

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 following table reports the relationship between these two variables for a random sample of 267 college students.

The given table of information is,

 Political views Class Standing Totals Freshmen and Sophomore Juniors and seniors Liberal 40 43 83 Moderate 50 50 100 Conservative 44 40 84 Totals 134 133 267

Steps:

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 83 for row marginal, 134 for column marginal and 267 for N in equation (1).

f1=83×134267=41.66

Substitute 83 for row marginal, 133 for column marginal and 267 for N in equation (1).

f2=83×133267=41.34

Substitute 100 for row marginal, 134 for column marginal and 267 for N in equation (1).

f3=100×134267=50.19

Substitute 100 for row marginal, 133 for column marginal and 267 for N in equation (1).

f4=100×133267=49.81

Substitute 84 for row marginal, 134 for column marginal and 267 for N in equation (1).

f5=84×134267=42.16

Substitute 84 for row marginal, 133 for column marginal and 267 for N in equation (1).

f6=84×133267=41.84

Consider the following table,

 fo fe fo−fe (fo−fe)2 (fo−fe)2/fe 40 41.66 −1.66 2.76 0.066 43 41.34 1.66 2.76 0.067 50 50.19 −0

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