In: Statistics and Probability
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.)
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.