Eating Out Vegetarian. Refer to the study on ordering vegetarian considered in Examples 12.8–12.10.

a. Without making a guess for the observed values of the sample proportions, find the common sample size that will ensure a margin of error of at most 0.01 for a 90% confidence interval. Hint:

Use Exercise 12.133.

b. Find a 90% confidence interval for p1 − p2 if, for samples of the size determined in part (a), 38.3% of the men and 43.7% of the women sometimes order veg.

c. Determine the margin of error for the estimate in part (b), and compare it to the required margin of error specified in part (a).