Question

In the book Business Research Methods (5th ed.), Donald R. Cooper and C. William Emory discuss a market researcher for an automaker who is studying consumer preferences for styling features of larger sedans. Buyers, who were classified as “first-time” buyers or “repeat” buyers, were asked to express their preference for one of two types of styling—European styling or Japanese styling. Of 40 first-time buyers, 7 preferred European styling and 33 preferred Japanese styling. Of 60 repeat buyers, 42 preferred European styling, and 18 preferred Japanese styling.

(a) Set up a contingency table for these data.

	Style
Buyers	European	Japanese	Total
First-time
Repeat
Total		__ans6__

(b) Test the hypothesis that buyer status (repeat versus first-time) and styling preference are independent at the .05 level of significance. What do you conclude? (Round your answer to 3 decimal places.)

χ2χ2 = (Click to select)RejectDo not reject H0: independence.

Answer 1

(a)

Contingency Table for these data is calculated as follows:

	European	Japanese	Total
First - time	7	33	40
Repeat	42	18	60
Total	49	51	100

(b)

Expected Frequency Table for these data is calculated as follows:

	European	Japanese	Total
First - time	49X40/100=19.60	51X40/100=20.40	40
Repeat	49X60/100=29.40	51X60/100=30.60	60
Total	49	51	100

Test Statistic is calculated as follows:

Observed Frequency (O)	Expected Frequency (E)	(O - E)2/E
7	19.60	8.100
33	20.40	7.782
42	29.40	5.400
18	30.60	5.188
Total = =		26.47

Test Statistic = 26.470

ndf = (r-1) X (c - 1)

    = (2 - 1) X (2 - 1)

    = 1

By Technology, p - value < 0.00001

Since p - value is less than = 0.05,the difference is significant. Reject null hypothesis.

Correct option:

Reject H0: independence