In the book Essentials of Marketing Research , William R. Dillon, Thomas J. Madd

Question

In the book Essentials of Marketing Research, William R. Dillon, Thomas J. Madden, and Neil A. Firtle discuss the relationship between delivery time and computer-assisted ordering. A sample of 40 firms shows that 16 use computer-assisted ordering, while 24 do not. Furthermore, past data are used to categorize each firm’s delivery times as below the industry average, equal to the industry average, or above the industry average. The results obtained are given in the table below.

A Contingency Table Relating Delivery Time and Computer-Assisted Ordering

(a) Test the hypothesis that delivery time performance is independent of whether computer-assisted ordering is used. What do you conclude by setting = .05?

(Click to select)Do not rejectReject H0: independence.

(b) Verify that a chi-square test is appropriate.

(c) Is there a difference between delivery-time performance between firms using computer-assisted ordering and those not using computer-assisted ordering?

Computer-
Assisted
Ordering Below
Industry
Average Delivery Time
Equal to
Industry
Average Above
Industry
Average Row
Total No 4 12 8 24 Yes 10 4 2 16 Column total 14 16 10 40

Explanation / Answer

Ans:

df=(2-1)*(3-1)=2

p-value= CHIDIST(8.929,2)=0.0115

As,p-value<0.05,we reject null hypothesis.

There is sufficient evidence to conclude that there is difference between delivery-time performance between firms using computer-assisted ordering and those not using computer-assisted ordering.

So,correct answer will be Yes.

Observed(O) Computer- Below Delivery Time Above Row Assisted Industry Equal to Industry Total Ordering Average Industry Average Average No 4 12 8 24 Yes 10 4 2 16 Column total 14 16 10 40 Expected(E) Assisted Industry Equal to Industry Total Ordering Average Industry Average Average No 8.4 9.6 6 24 Yes 5.6 6.4 4 16 Column total 14 16 10 40 Chi square=(O-E)^2/E 2.305 0.600 0.667 3.457 0.900 1.000 Total chi square score=8.929

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