A market researcher for an automobile company suspects differences in preferred

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 Silver Black Red Male 482 546 479 Female 278 310 357 a. Choose the competing hypotheses to determine whether color preference depends on gender. Ho. color preference is independent of gender, HA: Color preference is dependent on gender Ho: 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 d-1. What is the conclusion? Do not reject Ho; there is not enough evidence to support the claim that color preference is not independent Reject Ho; there is not enough evidence to support the claim that color preference is not independent Do not reject Ho; there is enough evidence to support the claim that color preference is not independent. Reject Ho, there is enough evidence to support the claim that color preference is not independent.

Explanation / Answer

a) Ho: color preference is independent of gender. ........

b)

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

for2 df and 0.01 level critical value =9.210

c) applying ch square test:

test statistic =9.31

d-1) as test statistic is higher than critical value :

reject Ho: there is enough evidence .,...............

Observed Oi male female Total silver 482 278 760 black 546 310 856 red 479 357 836 Total 1507 945 2452 Expected Ei=row*column/total male female Total silver 467.096 292.904 760 black 526.098 329.902 856 red 513.806 322.194 836 Total 1507 945 2452 chi square =(Oi-Ei)2/Ei male female Total silver 0.4755 0.7583 1.234 black 0.7529 1.2006 1.954 red 2.3578 3.7600 6.118 Total 3.586 5.719 9.31

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