Problems

1. Are men and women equally likely to say that a major reason they use Facebook is to share with many people at once? A survey reported that 42% of men (193 out of 459 sampled) and 50% of women (250 out of 501 sampled) said that a major reason they use Facebook is to share with many people at once. (Source: "6 new facts about Facebook," bit.ly/IrCTr00.)

At the 0.05 level of significance, is there evidence of a difference between men and women in the proportion that say that a major reason they use Facebook is to share with many people at once?

2. The owner of a restaurant that serves continental-style entrees wants to learn more about the patterns of patron demand during the Friday-to-Sunday time period. She has decided to study the demand for dessert during this period. In addition to studying whether a dessert was ordered, she will study whether a beef entree was ordered. Data were collected from 630 customers. Of the 197 patrons who ordered a beef entree, 74 ordered dessert. Of the 433 patrons who did not order a beef entree, 68 ordered dessert.

At the 0.05 level of significance, is there evidence of a difference in the proportion who order dessert based on whether they ordered a beef entree?

3. Do people trust banks to do what is right? A survey done in the United States and Japan revealed that, of 500 respondents in the United States, 250 said that they trusted banks to do what is right; in Japan, of 200 respondents, 120 said that they trusted banks to do what is right. (Source: E Norris, "Where Banking Crisis Raged, Trust Is Slow to Return," The New York Times, 26 January 2013, p. B3.)

At the 0.05 level of significance, is there evidence of a difference between respondents in the United States and Japan who trust banks to do what is right?

4. 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. (Source: "Drilling Down, Sizing Up a Cheeseburger's Caloric Heft," The New York Times, 4 October 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. Also suppose that 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 there is a difference in the mean estimated number of calories in the cheeseburger for the people who thought about the cheesecake first and for the people who thought about the organic fruit salad first.