Probability and Statistics for Engineering and the Sciences STAT 400 - University Of Maryland
Probability and Statistics for Engineering and the Sciences STAT 400 - University Of Maryland
9th Edition
ISBN: 9781305764477
Author: Jay L. Devore
Publisher: Cengage Learning
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Chapter 15.3, Problem 22E

Compute a 99% CI for μ1 − μ2 using the data in Exercise 12.

12. The article “A Study of Wood Stove Particulate Emissions” (J. of the Air Pollution Control Assoc., 1979: 724-728) reports the following data on bum time (hours) for samples of oak and pine. Test at level .05 to see whether there is any difference in true average bum time for the two types of wood.

Oak 1.72 .67 1.55 1.56 1.42 1.23 1.77 .48
Pine .98 1.40 1.33 1.52 .73 1.20
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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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Probability and Statistics for Engineering and the Sciences STAT 400 - University Of Maryland

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