STAT TECH IN BUSINESS & ECON AC
STAT TECH IN BUSINESS & ECON AC
18th Edition
ISBN: 9781264731657
Author: Lind
Publisher: MCG
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Chapter 8, Problem 4E

Listed next are the 27 Nationwide Insurance agents in the El Paso, Texas metropolitan area. The agents are numbered 00 through 26. We would like to estimate the mean number of years employed with Nationwide.

Chapter 8, Problem 4E, Listed next are the 27 Nationwide Insurance agents in the El Paso, Texas metropolitan area. The

  1. a. We want to select a random sample of four agents. The random numbers are 02, 59, 51, 25, 14, 29, 77, 69, and 18. Which dealers would be included in the sample?
  2. b. Use the table of random numbers to select your own sample of four agents.
  3. c. Using systematic random sampling, every fifth dealer is selected starting with the third dealer in the list. Which dealers are included in the sample?
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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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