Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card
Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card
13th Edition
ISBN: 9781337127264
Author: David R. Anderson, Dennis J. Sweeney, Thomas A. Williams, Jeffrey D. Camm, James J. Cochran
Publisher: Cengage Learning
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Chapter 11.1, Problem 4E

The variance in drug weights is critical in the pharmaceutical industry. For a specific drug, with weights measured in grams, a sample of 18 units provided a sample variance of s2 = .36.

  1. a. Construct a 90% confidence interval estimate of the population variance for the weight of this drug.
  2. b. Construct a 90% confidence interval estimate of the population standard deviation.
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iid 1. The CLT provides an approximate sampling distribution for the arithmetic average Ỹ of a random sample Y₁, . . ., Yn f(y). The parameters of the approximate sampling distribution depend on the mean and variance of the underlying random variables (i.e., the population mean and variance). The approximation can be written to emphasize this, using the expec- tation and variance of one of the random variables in the sample instead of the parameters μ, 02: YNEY, · (1 (EY,, varyi n For the following population distributions f, write the approximate distribution of the sample mean. (a) Exponential with rate ẞ: f(y) = ß exp{−ßy} 1 (b) Chi-square with degrees of freedom: f(y) = ( 4 ) 2 y = exp { — ½/ } г( (c) Poisson with rate λ: P(Y = y) = exp(-\} > y! y²
2. Let Y₁,……., Y be a random sample with common mean μ and common variance σ². Use the CLT to write an expression approximating the CDF P(Ỹ ≤ x) in terms of µ, σ² and n, and the standard normal CDF Fz(·).
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Bundle: Statistics for Business & Economics, Loose-leaf Version, 13th + MindTap Business Statistics with XLSTAT, 2 terms (12 months) Printed Access Card

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