Expand Your Knowledge: Sample Size, Difference of Means What about sample size? If we want a confidence interval with maximal margin of error E and level of confidence

c, then Section 7.1 shows us which formulas to apply for a single mean m and Section 7.3 shows us formulas for a single proportion p.

(a) How about a difference of means? When s1 and s2 are known, the margin of error E for a c%

confidence interval is

Let us make the simplifying assumption that we have equal sample sizes n so that n 5n1 5n2. We also assume that n $ 30. In this context, we get

(b) In Problem 18 (football and basketball player heights), suppose we want to be 95% sure that our estimate x1 2x2 for the difference m1 2m2 has a margin of error E 5 0.05 foot. How large should the sample size be (assuming equal sample size—
i.e., n 5n1 5n2)? Since we do not know s1 or s2 and n $ 30, use s1 and s2, respectively, from the preliminary sample of Problem 18.

(c) In Problem 19 (petal lengths of two iris species), suppose we want to be 90% sure that our estimate x1 2x2 for the difference m1 2m2 has a margin of error E 5 0.1 cm. How large should the sample size be (assuming equal sample size—i.e., n 5n1 5n2)? Since we do not know s1 or s2 and n $ 30, use s1 and s2, respectively, from the preliminary sample of Problem 19.AppendixLO1

E=Zc n n