Question

In: Statistics and Probability

A market researcher for an automobile company suspects differences in preferred color between male and female...

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.)

Solutions

Expert Solution

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.


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