Refer to the Journal of Marketing Research (Dec., 2011) study of shopping cart design, Exercise 8.41. Recall that design engineers want to know whether the mean choice of 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 y̅₁ = 59, while the average for the n₂ = 11 consumers with an extended arm was y̅₂ = 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.

Data from Exercise 8.41

Refer to the Journal of Marketing Research (Dec., 2011) study of shopping cart design. Design engineers want to know whether you may be more likely to purchase a vice product (e.g., a candy bar) when your arm is flexed (as when carrying a shopping basket) than when your arm is extended (as when pushing a shopping cart). To test this theory, the researchers recruited 22 consumers and had each push their hand against a table while they were asked a series of shopping questions. Half of the consumers were told to put their arm in a flex position (similar to a shopping basket) and the other half were told to put their arm in an extended position (similar to a shopping cart). Participants were offered several choices between a vice and a virtue (e.g., a movie ticket vs. a shopping coupon, pay later with a larger amount vs. pay now) and a choice score (on a scale of 0 to 100) was determined for each. (Higher scores indicate a greater preference for vice options.) The average choice score for consumers with a flexed arm was 59, while the average for consumers with an extended arm was 43.