Refer to the Journal of Marketing Research (Dec., 2011) study of shopping cart design, Exercise 2.43. 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. 

a. Suppose the standard deviations of the choice scores for the flexed arm and extended arm conditions are 4 and 2, respectively. In Exercise 2.43a you were asked whether this information supports the researchers’ theory. Now answer the question by conducting a hypothesis test. Use α = .05.

b. Suppose the standard deviations of the choice scores for the flexed arm and extended arm conditions are 10 and 15, respectively. In Exercise 2.43b you were asked whether this information supports the researchers’ theory. Now answer the question by conducting a hypothesis test. Use α = .05.

Data from Exercise 2.43

Engineers who design shopping vehicles (e.g., carts) for retail stores take into account issues such as maneuverability, shopping behavior, child safety, and maintenance cost. Interestingly, while shopping at the grocery store you may be more likely to buy a vice product (e.g., a candy bar) when pushing a shopping cart than when carrying a shopping basket. This possibility was explored in the Journal of Marketing Research (Dec., 2011). The researchers believe that when your arm is flexed (as when carrying a basket) you are more likely to choose a vice product than when your arm is extended (as when pushing a cart). To test this theory in a laboratory setting, the researchers recruited 22 consumers and had each push their hand against a table while they were asked a serious 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.