You are conducting a test of independence for the claim that there is an association between the row

Juliet Jackson

Juliet Jackson

Answered question

2022-03-06

You are conducting a test of independence for the claim that there is an association between the row variable and the column variable.
 X  Y  Z  A 35296 B 53385
The expected observations for this table would be
 X  Y  Z  A  B 
What is the chi-square test-statistic for this data? (2 decimals) χ2=
Report all answers accurate to two decimal places.

Answer & Explanation

Misurina6am

Misurina6am

Beginner2022-03-07Added 2 answers

From the given information, it is clear that,
The observed data are,
 X  Y  Z  Total  A 3529670 B 5338596 Total 886711166
We have to find the chi-square test statistic ,
Formula for the chi-square test statistic is,
χ2=(OiEi)2Ei
Where Oi is observed value and Ei is expected value
First we have to calculate the expected values,
Formula for the expected value is,
E=Row total×column totalTotal
 X  Y  Z  A 70(88)166=37.1170(67)166=28.2570(11)166=4.64 B 96(88)166=50.8996(77)166=38.7596(11)166=6.36
Now, we have to calculate the chi-square test statistic,
That is,
 X  Y  Z  A (3537.11)237.11=0.1199(2928.25)228.25=0.0265(64.64)24.64=1.8496 B (5350.89)250.89=0.0875(3838.75)238.75=0.0145(56.36)26.36=0.2908

Brock Floyd

Brock Floyd

Beginner2022-03-08Added 2 answers

Therefore, the chi-square test statistic is,
χ2=(OiEi)2Ei
=0.1199+0.0265+1.8496+0.0875+0.0145+0.2908
=2.3888
=2.39
Hence, it is clear that, the chi-square test statistic value is 2.39

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