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 15.1, Problem 5E

Both a gravimetric and a spectrophotometric method are under consideration for determining phosphate content of a particular material. Twelve samples of the material are obtained, each is split in half, and a determination is made on each half using one of the two methods, resulting in the following data:

Sample 1 2 3 4
Gravimetric 54.7 58.5 66.8 46.1
Spectrophotometric 55.0 55.7 62.9 45.5
Sample 5 6 7 8
Gravimetric 52.3 74.3 92.5 40.2
Spectrophotometric 51.1 75.4 89.6 38.4
Sample 9 10 11 12
Gravimetric 87.3 74.8 63.2 68.5
Spectrophotometric 86.8 72.5 62.3 66.0

Use the Wilcoxon test to decide whether one technique gives on average a different value than the other technique for this type of material.

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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
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