Question

A market researcher for an automobile company suspects differences in preferred color between male and female buyers. Advertisements targeted to different groups should take such differences into account, if they exist. The researcher examines the most recent sales information of a particular car that comes in three colors. Use Table 3.

	Gender of Automobile Buyer
Color	Male	Female
Silver	490	298
Black	537	290
Red	492	348

a.	Choose the competing hypotheses to determine whether color preference depends on gender.
	H0: Color preference is independent of gender; HA: Color preference is dependent on gender. H0: Color preference is dependent on gender; HA: Color preference is independent of gender.

b.	Find the critical value at the 1.0% significance level. (Round your answer to 2 decimal places.)

Critical value

c.	Calculate the value of the test statistic. (Round the intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Test statistic

Answer 1

a)H0: Color preference is independent of gender; HA: Color preference is dependent on gender.

b)

degree of freedom =(row-1)*(column-1)=(2-1)*(3-1)=2

for 2 df and 0.01 level ; critical value =9.21

c)

applying chi square test:

Observed	OBS	silver	black	red	Total
	male	490	537	492	1519
	female	298	290	348	936
	Total	788	827	840	2455
Expected	Ei=?row*?column/?total	silver	black	red	Total
	male	487.565	511.696	519.739	1519
	female	300.435	315.304	320.261	936
	Total	788	827	840	2455
chi square	=(Oi-Ei)2/Ei	silver	black	red	Total
	male	0.01	1.25	1.48	2.74
	female	0.02	2.031	2.403	4.45
	Total	0.03	3.28	3.88	7.197

Test statistic =7.20