Test whether the contingency table has independent row and column variables. The critical value is with one degree of freedom is X2r = 7.879.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 6E
Question
100%

Test whether the contingency table has independent row and column variables. The critical value is with one degree of freedom is X2= 7.879.

392 13
564 57
Expert Solution
Step 1

Here, use chi square test for independence of two categorical variables.

The hypothesis will be as follows:

Null hypothesis: H0: Two categorical variables are independent.

Alternative hypothesis: Ha: Two categorical variables are dependent.

 

Assume level of significance = α= 0.005

 

Test statistic formula is given as below:

Chi square =O-E2E

Where, O is observed frequencies and E is expected frequencies.

E=Row total×Column totalGrand total

 

Step 2

Given here,

Number of rows = r = 2

Number of columns = c = 2

Degrees of freedom =df = (r  1)×(c  1) = 1×1 = 1

α = 0.005

Critical value = 7.879439

(by using Chi square table)

 

Step 3

Calculation tables for test statistic are given as below:

Observed Frequencies

     

 

 

Column variable

   

Calculations

 

Row variable

C1

C2

Total

 

(O - E)

 

R1

392

13

405

 

14.63158

-14.6316

R2

564

57

621

 

-14.6316

14.63158

Total

956

70

1026

     

                                                                                                          

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