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. a. Choose the competing hypotheses to determine whether color preference depends on gender. H_0: Color preference is independent of gender.: H_A: Color preference is dependent on gender. H_0: Color preference is dependent on gender.: H_A: Color preference is independent of gender. b. Find the critical value at the 1% 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 What is the conclusion? Reject H_0: there is enough evidence to support the claim that color preference is not independent. Reject H_0: there is not enough evidence to support the claim that color preference is not independent. Do not reject H_0: there is enough evidence to support the claim that color preference is not independent. Do not reject H_0: there is not enough evidence to support the claim that color preference is not independent. Does your conclusion suggest that the company should target advertisements differently for males versus females? Yes No

Explanation / Answer

a)

Ho: color preference is independent of gender

b)

critical value = X^2(0.01,4) = 9.21

d1)

d) do not reject H0 , there is not enough evidence to support the claim that color preference is not independent

d-2)

No

color male female total silver 470 280 750 black 535 285 820 red 495 350 845 total 1500 915 2415 Expected frequecy col1 col2 row1 465.8385093 284.1614907 row2 509.3167702 310.6832298 row3 524.8447205 320.1552795 observed expected (O-E)^2/E 470 465.8385093 0.03717598344 280 284.1614907 0.06094423514 535 509.3167702 1.295123845 285 310.6832298 2.123153844 495 524.8447205 1.697087361 350 320.1552795 2.782110428 Test static 7.995595696

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