Expand Your Knowledge: Sample Size, Difference of Means

Chapter , Problem 24

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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 8.1 shows us which formulas to apply for a single mean m and Section 8.3 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 n1 n2. Also assume that In this context, we get Solve this equation for n and show that (b) In (football and basketball player heights), suppose we want to be 95% sure that our estimate for the difference m1 m2 has a margin of error E 0.05 feet. How large should the sample size be (assuming equal sample size, i.e., n n1 n2)? Since we do not know s1 or s2 and n 30, use s1 and s2, respectively, from the preliminary sample of 11. (c) In (petal lengths of two iris species), suppose we want to be 90% sure that our estimate for the difference m1 m2 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 s1 or s2 and n 30, use s1 and s2, respectively, from the preliminary sample of 12. 25.