Question

Perform Chi-squared test of independence. The significance level alpha is 5%.

Columns: category 1

Rows: categoty 2

Contingency table

67   26    16

128   63    46

1. DF=
2. Ch-square, round to three decimal places=
3. p-value, round to three decimal places=
4. Conclusions: based on the results, do you think the these two variables are dependent or independent? Enter the correct answer using the following options:  (type the corresponding capital letter, do not type the "dot" at the end)
   1. Not independent at 5% significance level.
   2. Independent with 95% confidence.
   3. Do not reject that they are independent at 5% significance level and reserve judgement. We may accept independence, but with some unknown probability.
   4. Reject both, H0 and H1, the test has failed.
   5. Accept both, H0 and H1, the test has failed.

Answer 1

a)

degree of freedom(df) =(rows-1)*(columns-1)=

2

b)

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	c	d	e	Total
	a	61.431	28.038	19.532	109
	b	133.569	60.962	42.468	237
	total	195	89	62	346
chi square    χ2	=(Oi-Ei)2/Ei	c	d	e	Total
	a	0.505	0.148	0.639	1.2916
	b	0.232	0.068	0.294	0.5940
	total	0.7371	0.2162	0.9323	1.8857
test statistic X2=		1.886

c)

p value =

0.390

from excel: chidist(1.8857,2)

d)

since p value >0.05

option C is correct

Do not reject that they are independent at 5% significance level and reserve judgement. We may accept independence, but with some unknown probability.