Chapter 12.1, Problem 59E

Asthmatics and Sulfites. Refer to Exercise 12.51.

1.                                            a.      Determine the margin of error for the estimate of p.
2.                                            b.      Obtain a sample size that will ensure a margin of error of at most 0.01 for a 95% confidence interval without making a guess for the observed value of $\hat{p}$.
3.                                             c.      Find a 95% confidence interval for p if, for a sample of the size determined in part (b), the proportion of asthmatics sampled who are allergic to sulfites is 0.071.
4.                                            d.      Determine the margin of error for the estimate in part (c) and compare it to the margin of error specified in part (b).
5.                                             e.      Repeat parts (b)–(d) if you can reasonably presume that the proportion of asthmatics sampled who are allergic to sulfites will be at most 0.10.
6.                                              f.      Compare the results you obtained in parts (b)–(d) with those obtained in part (e).