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Statistics For Business And Economics
Found in: Page 501
Statistics For Business And Economics

Statistics For Business And Economics

Book edition 13th
Author(s) James T. McClave, P. George Benson, Terry Sincich
Pages 888 pages
ISBN 9780134506593

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Short Answer

Shopping vehicle and judgment. Refer to the Journal of Marketing Research (December 2011) study of shopping cart design, Exercise 2.85 (p. 112). Recall that design engineers want to know whether the mean choice of the vice-over-virtue score is higher when a consumer’s arm is flexed (as when carrying a shopping basket) than when the consumer’s arm is extended (as when pushing a shopping cart). The average choice score for the n1 = 11 consumers with a flexed arm was x¯1= 59, while the average for the n2 = 11 Consumers with an extended arm was x¯2 = 43. In which scenario is the assumption required for a t-test to compare means more likely to be violated, S1 = 4 and S2 = 2, or, S1 = 10 and S2 = 15? Explain.

The answer can be reduced from the following steps.

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Step by Step Solution

Step 1: Given information

Referring to Exercises 8.8 and 8.9, there is no difference between the n1 and n2 consumers' average scores. The sample mean of consumers with a flexed arm and extended arm was different, that is x¯1= 59, x¯2 = 43. The standard deviation in consumers with a flexed arm and consumers with an extended are dissimilar.

Step 2: Explaining the t-test

A statistical test called a t-test is employed to contrast the means of two clusters. It is frequently employed in hypothesis testing to establish whether one procedure or treatment affects the target group or even if two groups vary.

The two different kinds of t-tests are as follows.

  • Use a two-tailed t-test if the only thing that matters is how the two populations vary from each other.
  • Use a one-tailed t-test to determine if one population mean is higher or lower compared to the other.

Step 3: Validation of the t-test's premise

t-test hypotheses are as follows


The application of test statistics is as follows.


Following is test statistics with the degree of freedom.

df = n1 - 1and df = n2 - 1 are similar because of the mean of consumers with a flexed arm and extended arm are similar. As H0:μ1=μ2and n1 = n2, reject the claim that the value of t is higher. Therefore, the hypothesis will most likely be rejected if S1 and S2 are lower.

Case-1: If S1 = 4and S2 = 2

The test statistics is as follows.


Case-2: If S1 = 10 and S2 = 15


The p-value for case 1 will be higher than case 2 as t increases. In case 1, it is more likely that the hypotheses will be rejected.

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