Question

You are conducting a test of the claim that the row variable and the column variable are dependent in the following contingency table.

	X	Y	Z
A	38	2	42
B	43	17	30

Give all answers rounded to 3 places after the decimal point, if necessary.

Enter the expected frequencies below:

	X	Y	Z
A
B

(b) What is the chi-square test-statistic for this data?
      Test Statistic: χ2=

Answer 1

The table for observed frequency is ,

	X	Y	Z	Total
A	38	2	42
B	43	17	30
Total				N=172

The table for expected frequency is ,

  ; i=1,2 and j=1,2,3

	X	Y	Z
A	38.616	9.058	34.326
B	42.384	9.942	37.674

(b)

The chi-square test statistic is ,

The table for is ,

	X	Y	Z
A	37.394	0.442	51.39
B	43.625	29.07	23.889

Therefore ,

Critical value : ; From excel "=CHIINV(0.025,2)"

Where , d.f.=Degrees of Freedom=(r-1)(c-1)=(2-1)*(3-1)=2