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 (1 and (2 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 = n1 = n2. We also assume that n ( 30. In this context, we get
Solve this equation for n and show that
(b) In Problem 15 (football and basketball player heights), suppose we want to be 95% sure that our estimate x̅1 - x̅2 for the difference (1 - (2 has a margin of error E - 0.05 foot. How large should the sample size be (assuming equal sample size- i.e., n = n1 = n2)? Since we do not know (1 or (2 and n ( 30, use s1 and s2, respectively, from the preliminary sample of Problem 15.
(c) In Problem 16 (petal lengths of two iris species), suppose we want to be 90% sure that our estimate x̅1 - x̅2 for the difference (1 - (2 has a margin of error E = 0.1 cm. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)? Since we do not know (1 or (2 and n ( 30, use s1 and s2, respectively, from the preliminary sample of Problem 16.
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