Do men and women prefer the same colors of cars? That is, is sex independent of

Question

Do men and women prefer the same colors of cars? That is, is sex independent of color preference for cars? Suppose a study is undertaken to address this question. A random sample of men and women are asked which of five colors (silver, white, black, green, blue) they prefer in a car. The results as analyzed using Minitab are shown here. Discuss the test used, the hypotheses, the findings, and the business implications.

Chi uare Test: Men, Women Expected counts are printed below observed counts Chi-square contributions are printed below expected counts. Men Women Total 142 85.20 56.80 0.270 0.406 133 79.80 53.20 0.289 0.433 63 93 55.80 37.20 0.929 1.394 43.20 28.80 0.408 0.612 36.00 24.00 0.250 0.375 Total 300 200 500 Chi-Sq m 5.366, DF 4, P-value 0.252

Explanation / Answer

We have to test the null hypothesis

H0: Sex is independent of color preference of cars

Versus the alternative hypothesis

Ha: Sex is dependent of color preference of cars

For this chi-square test of independence is applied and the results showed that all cells have expected count greater than 5, so assumption of chi-square test is satisfied. We have not enough evidence to reject the null hypothesis 2(4)=5.37, p=0.252>0.05. Hence sex is independent of color preference of cars so the business implication is that there is no need to care for color preference difference amongst male and female.

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