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 exed (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 24 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 ex 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 O to 100) was determined for each. (Higher scores indicate a greater preference for vice options.) The average choice score for consumers with a exed arm was 62, while the average for consumers with an extended arm was 46. Suppose the standard deviations of the choice scores for the exed arm and extended arm conditions are 6 and 2, respectively. Does this information support the researchers' theory? Answer the question by conducting a hypothesis test. Use 0: = 0.05. Test the claim about the difference between two population means u, and u, at the level of significance . Assume the samples are random and independent, and the populations are normally distributed. Claim: H1 = H2; 0 = 0.01 Population statistics: 61 = 3.6, 62 = 1.5 Sample statistics: X, = 16, n1 = 29, X2 = 18, n2 = 28A study was conducted to determine who is more likely to offer windrowing (mowing and piling) of hay services, producers in State A or producers in State B. Of the 558 producers from State A, 182 were willing to offer windrowing services. 01' the 937 producers from State B, 388 were willing to offer windrowing services. The researchers want to know if the proportion of producers who were willing to offer windrowing services differs for the two areas, State A and State B. Complete parts a