In this exercise, apply Formulas 11.3 and 11.4 on pages 466 and 467 to the study on ordering vegetarian considered in Examples 11.8–11.10.
a. Obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by taking half the length of the confidence interval found in Example 11.10 on page 46
6. Interpret your answer in words.
b. Obtain the margin of error for the estimate of the difference between the proportions of men and women who sometimes order veg by applying Formula 11.3.
c. 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.
d. Find a 90% confidence interval for p1 − p2 if, for samples of the size determined in part (c), 38.3% of the men and 43.7% of the women sometimes order veg.
e. Determine the margin of error for the estimate in part (d), and compare it to the required margin of error specified in part (c).
f. Repeat parts (c)–(e) 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.
g. Compare the results obtained in parts (c)–(e) to those obtained in part (f).