Test whether the contingency table has independent row and column variables. The critical value is with one degree of freedom is X2r = 7.879.
392
13
564
57
Definition Definition Visual representation of the relationship between two or more categorical variables. A contingency table is a categorical version of the scatterplot, which is used to visualize the linear relationship between two variables.
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 = = 0.005
Test statistic formula is given as below:
Chi square =
Where, O is observed frequencies and E is expected frequencies.
Step 2
Given here,
Number of rows = r = 2
Number of columns = c = 2
Degrees of freedom =
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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