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)RejectDo not reject 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

(a) H0 : delivery time performance is independent of whether computer-assisted ordering is used

Ha : delivery time performance is not independent of whether computer-assisted ordering is used

Observed Table

Expected Table

Expected Value is calculated by i.e.

Expected value of No and Below industry average = Total No * Toal below industry average/ Total sample = 14 * 24/40

Now chi- square statistic

X2 = (oi - Ei)2/Ei = 8.93

so here degree of freedom = 1 * 2 = 2 and alpha = 0.05

X2 criticial = 5.9914

so X2 > X2 criticial  so we shall reject the null hypothesis and can claim that delivery time performance is not independent of whether computer-assisted ordering is used.

(b) The test is valid because the number of cells exceeds 3, the average of the Êij is greater
than 5 and the smallest Êij is greater than 1 .

(c) Yes, there is a difference between delivery-time performance between firms using computer-assisted ordering and those not using computer-assisted ordering as we have rejected the null hypothesis.

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

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