Question

cite and explain how chi square is utilized in stat analysis by giving an example including constructing a 2x2 table

Answer 1

Ans:

Chi-square Test of Independence is used to check the relationship between two variables(whether independent or dependent).

H₀: In the population, the two categorical variables are independent.
H_a: In the population, two categorical variables are dependent.

	Observed count(fo)
	favor	opposed	total
democrat	138	64	202
republican	64	84	148
total	202	148	350
	Expected count(fe)
	favor	opposed	total
democrat	116.58	85.42	202
republican	85.42	62.58	148
total	202	148	350
	Chi square=(O-E)^2/E
	favor	opposed	total
democrat	3.934	5.370	9.305
republican	5.370	7.329	12.699
total	9.305	12.699	22.004

Test statistic:

Chi square=22.004

df=(2-1)*(2-1)=1

p-value=chidist(22.004,1)=0.0000

As,p-value<0.05,we reject the null hypothesis.There is sufficient evidence to conclude that two categorical variables are dependent.