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. (You may find it useful to reference the appropriate table: chi-square table or F table)

	Sex of Automobile Buyer
Color	Male	Female
Silver	477	298
Black	536	308
Red	482	348

b-1. Calculate the value of the test statistic. (Round the intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Answer 1

Use Chi-Square test and solve using Excel in the following manner:

	ACTUAL
	Male	Female	Total
Silver	477	298	775
Black	536	308	844
Red	482	348	830
Total	1495	954	2449
	EXPECTED
	Male	Female		FORMULA FOR EXPECTED VALUE
Silver	473.1013	301.8987		=(B$6*$D3)/$D$6	=(C$6*$D3)/$D$6
Black	515.2225	328.7775		=(B$6*$D4)/$D$6	=(C$6*$D4)/$D$6
Red	506.6762	323.3238		=(B$6*$D5)/$D$6	=(C$6*$D5)/$D$6
	CHI-SQUARE
	Male	Female		FORMULA FOR CHI-SQUARE
Silver	0.0321	0.0503		=(B3-B10)^2/B10	=(C3-C10)^2/C10
Black	0.8379	1.3131		=(B4-B11)^2/B11	=(C4-C11)^2/C11
Red	1.2018	1.8833		=(B5-B12)^2/B12	=(C5-C12)^2/C12
Test statistic	5.319	=SUM(B16:C18)
Critical value	5.991	=CHISQ.INV.RT(0.05,2)

H₀: There are no differences in preferred color between male and female buyers

H₁: There are differences in preferred color between male and female buyers

Test statistic = 5.319

Degrees of freedom: df = (Rows-1)*(Columns-1) = (3-1)*(2-1) = 2

Level of significance = 0.05

Critical value (Using Excel function CHISQ.INV.RT(probability, df)) = CHISQ.INV.RT(0.05,2) = 5.991

Since test statistic is less than critical value, we do not reject the null hypothesis.

So, there are no differences in preferred color between male and female buyers.