Design engineers want to know whether you may be more likely to purchase a vice product (for example, 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 1818 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 flexed 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 (for example, 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 60, while the average for consumers with an extended arm was 41. Suppose the standard deviations of the choice scores for the flexed arm and extended arm conditions are 10 and 10, respectively. Does this information support the researchers' theory? Answer the question by conducting a hypothesis test. Use alpha = 0.05. Specify the null and alternative hypotheses. Let the first group be the consumers assigned to the flex position, and let the second group be the consumers assigned to the extended position.
H0: μ1 - μ2 = 0
Ha: μ1 - μ2 ≠ 0
Compute the test statistic.
The test statistic is. (Round to two decimal places as needed.)
Compute the p-value.
p =. (Round to three decimal places as needed.)
Make a conclusion.
Reject the null hypothesis. There is not sufficient evidence that the difference in the population means is different than that given by the null hypothesis. Enter your answer in each of the answer boxes.