When Americans eat out at restaurants, most choose American food; however, tastes for Mexican, * Chinese, and Italian food vary from region to region of the United States. In a recent CBS telephone survey , it was found that 39% of families ate together 7 nights a week, slightly less than the 46% of families who reported eating together 7 nights a week in an earlier survey by CBS. Most Americans, both men and women, do some of the cooking when meals are cooked at home, as reported in the following table where we compare the number of evening meals personally cooked per week by men and women. Income How often Americans eat out at restaurants is largely a function of income. "While most households earning over $50,000 got restaurant food for dinner at least once in the last week, 75% of those earning under $15,000 did not do so at all." All Men Number of Meals Cooked Men Women Under $15,000 3. $15-$30,000 $30-$50,000 Over $50,000 Fast Food Nights With Kids Without Kids Fast Food Nights Women None 47 75 58 59 31 0 47 59 0 46 In spite of all the negative publicity about obesity and high calories associated with burgers and fries, many Americans continue to eat fast food to save time within busy schedules. 63 49 19 39 38 1-3 Nights 4 or More Nights 64 1 30 20 3 or Less 76 33 1 28 20 4 or More 2-3 19 16 24 67 2-3 20 15 4 6 3 3 5 4+ 4 5 4+ 6 2 Fifty-three percent of families with kids ate fast food at least once last week, compared with 41% of families without kids. Furthermore, 54% of men ate fast food at least once last week, compared with only 37% of women. The description of the survey methods that gave rise to this data was stated as follows: "This poll was conducted among a nationwide random sample of 936 adults, interviewed by telephone. The error due to sampling for results based on the entire sample could be plus or minus three percentage points." 1. Verify the margin of error of ±3 percentage points as stated for the sample of n = 936 adults. Suppose that the sample contained an equal number of men and women or 468 men and 468 women. What is the margin of error for men and for women? 2. Do the numbers in the tables indicate the number of people/families in the categories? If not, what do those numbers represent? a. Construct a 95% confidence interval for the proportion of Americans who ate together seven nights a week. b. Construct a 95% confidence interval for the difference in the proportion of women and men who personally cook at least 4+ meals per week. c. Construct a 95% confidence interval for the proportion of Americans who eat out at restaurants at least once a week. 4. If these questions were asked today, would you expect the responses to be similar to those reported here or would you expect them to differ significantly?