Repeat Exercise 12.136 by applying the formula in Exercise 12.134(a) if you can reasonably presume that at most 41% of the men sampled and at most 49% of the women sampled will be people who sometimes order veg. Compare the results obtained in Exercise 12.136 to those obtained here.
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.
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).