10.7 When people make estimates, they are influenced by anchors to their estimates. A study was conducted in which students were asked to estimate the number of calories in a cheeseburger. One group was asked to do this after thinking about a calorie-laden cheesecake. A second group was asked to do this after thinking about an organic fruit salad. The mean number of calories estimated in a cheeseburger was 780 for the group that thought about the cheesecake and 1,041 for the group that thought about the organic fruit salad. (Data extracted from “Drilling Down, Sizing Up a Cheeseburger’s Caloric Heft,” The New York Times, October 4, 2010, p. B2.) Suppose that the study was based on a sample of 20 people who thought about the cheesecake first and 20 people who thought about the organic fruit salad first, and the standard deviation of the number of calories in the cheeseburger was 128 for the people who thought about the cheesecake first and 140 for the people who thought about the organic fruit salad first. a. State the null and alternative hypotheses if you want to determine whether the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first. b. In the context of this study, what is the meaning of the Type I error? c. In the context of this study, what is the meaning of the Type II error? d. At the 0.01 level of significance, is there evidence that the mean estimated number of calories in the cheeseburger is lower for the people who thought about the cheesecake first than for the people who thought about the organic fruit salad first?
10.20 Nine experts rated two brands of Colombian coffee in a taste-testing experiment. A rating on a 7-point scale (1 = extremely unpleasing, 7 = extremely pleasing) is given for each of four characteristics: taste, aroma, richness, and acidity. The following data stored in Coffee contain the ratings accumulated over all four characteristics: a. At the 0.05 level of significance, is there evidence of a difference in the mean ratings between the two brands? b. What assumption is necessary about the population distribution in order to perform this test? c. Determine the p-value in (a) and interpret its meaning. d. Construct and interpret a 95% confidence interval estimate of the difference in the mean ratings between the two brands.
10.34 Does co-browsing have positive effects on the customer experience? Co-browsing refers to the ability to have a contact center agent and customer jointly navigate an online document or mobile application on a real-time basis through the web. A study of businesses indicates that 81 of 129 co-browsing organizations use skills-based routing to match the caller with the right agent, whereas 65 of 176 non-co-browsing organizations use skills-based routing to match the caller with the right agent. (Source: Cobrowsing Presents a ‘Lucrative’ Customer Service Opportunity, available at bit.ly/1wwALWr.) a. At the 0.05 level of significance, is there evidence of a difference between co-browsing organizations and non-co-browsing organizations in the proportion that use skills-based routing to match the caller with the right agent? b. Find the p-value in (a) and interpret its meaning.
