Question

A researcher wanted to examine if there is a relationship between color preference (i.e., favorite color: red, yellow, green or blue) and personality type (i.e., extrovert or introvert). He selected a sample of n = 200 participants; each participant took a personality test and identified the favorite color. The collected data are shown in the table below.

Do the data indicate a significant relationship between personality type and color preference? Test with p < .01.

	RED	YELLOW	GREEN	BLUE
INTROVERT	10	3	15	22
EXTROVERT	90	17	25	18

For full credit include:

• hypotheses
• calculation of expected frequency
• calculation of Chi² test
• df and critical value of Chi² used for hypothesis test
• decision about H₀
• full conclusion in APA format.

Answer 1

#solution:

Hypothesis

Ho:Colour preference and personality type are independent

Hao:Colour preference and personality type are dependent

	#observed frequency
		RED	YELLOW	GREEN	BLUE	Total
	INTROVERT	10	3	15	22	50
	EXTROVERT	90	17	25	18	150
	total	100	20	40	40	200
Expected	Ei=Σ corespondin row*Σcorespondin column/Σtotal	RED	YELLOW	GREEN	BLUE	Total
	INTROVERT	25	5	10	10	50
	EXTROVERT	75	15	30	30	150
	total	100	20	40	40	200
chi square    χ2	=(Oi-Ei)2/Ei	RED	YELLOW	GREEN	BLUE	Total
	INTROVERT	9	0.8	2.5	14.4	26.7
	EXTROVERT	3	0.266666667	0.833333333	4.8	8.9
	total	12	1.066666667	3.333333333	19.2	35.6

## chi square    χ2=sum(=(Oi-Ei)2/Ei)=35.6

df=(r-1)*(c-1)=(2-1)*(4-1)=3

critical value of Chi2=11.35---using Excell==CHIINV(0.01,3)

#test statistics > critical value hence we reject Ho at 1% l.o.s ie 35.6>11.35

#Conclusion:

Colour preference and personality type are dependent.

ie there is relationship between personality type and color preference