Question

A researcher is investigating the association between gender and favorite color with simple random sample of 1000 participants. Respondents were classified by gender (male or female) and by favorite color (Red, Blue, Yellow). Please state the hypothesis, analyze the data sample, and interpret the results below. (chi square)

               Red        Blue         Yellow

male        200       400            400

female     400        200          400

Answer 1

The null and alternate hypothesis are:

H0: Favourite color is independent of gender.
Ha: Favourite color is not independent of gender.

Observed (Oi):

	Red	Blue	Yellow	TOTAL
Male	200	400	400	1000
Female	400	200	400	1000
TOTAL	600	600	800	2000

Now, Expected frequency = [(Row total) x (Column total)] / Table total

Expected (Ei):

	Red	Blue	Yellow	TOTAL
Male		300	400	1000
Female	300	300	400	1000
TOTAL	600	600	800	2000

Test statistic value =

Let the level of significance be 0.05

The critical value is given by:

Since the test statistic value is greater than the critical value, so we have sufficient evidence to reject null hypothesis H0. Thus, we can say that favourite color is not independent of gender.