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Whatsamplesizeshouldbetakenassumethat

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Unformatted text preview: e determine the interval width first, and derive the required sample size. The phrase “estimate the mean to within e units”, translates to an interval estimate of the form s s x ±e Slide 17 Determining the Sample Size s The required sample size to estimate the mean is zα 2σ n= e s 2 The “e” is also known as the acceptable margin of error allowed. Slide 18 Determining the Sample Size s Example • To estimate the amount of lumber that can be harvested in a tract of land, the mean diameter of trees in the tract must be estimated to within one inch with 99% confidence. • What sample size should be taken? Assume that diameters are normally distributed with σ = 6 inches. Slide 19 Determining the Sample Size s Solution • The estimate accuracy is +/­1 inch. That is e = 1. • The confidence level 99% leads to α = .01, thus zα/2 = z.005 = 2.575. • We compute zα 2σ 2.575(6) 2 n= = = 239 1 e 2 If the standard deviation is really 6 inches, the interval resulting from the random...
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