Workshop20

# Workshop20 - CHEN 3010 Applied Data Analysis Names: Fall...

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CHEN 3010 Applied Data Analysis Fall 2004 Names: __________________________ __________________________ __________________________ __________________________ Workshop # 20 Excel's Data Analysis Tools for Hypothesis Testing Background Standard hypothesis tests can be categorized in a number of ways, but three classifications are most useful: 1) tests on means with known variance 2) tests on means with unknown variance 3) tests on variances of normal distributions In each of these categories, tests are of the following types: a) testing against a given value b) comparison of two data sets and are according to two types of alternate hypotheses: i) two-sided, not equal to ii) one-sided, less than or greater than The following three tables summarize the standard tests: Hypothesis Tests TABLE 1: tests on means with known variance H 0 H 1 test statistic criteria for rejection μμ = 0 0 Z x n 0 0 = μ σ ZZ 02 > α < 0 0 < > 0 0 > 12 = Z xx nn 0 1 2 1 2 2 2 = + σσ > < 0 < > 0 >

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CHEN 3010 Workshop #20 Page 2 TABLE 2: tests on means with unknown variance H 0 H 1 test statistic criteria for rejection μμ 0 t x sn 0 0 = μ tt n 02 1 > α , = 0 < 0 t t n 01 < , > 0 n > , 12 assuming equal variances > αν , = < t xx s nn p 0 11 = + 0 < , > ν =+ 2t t 0 > , assuming unequal variances > αγ , = < t s n s n 0 1 2 1 2 2 2 = + 0 < , > γ = + + INT s n s n s n n s n n 1 2 1 2 2 2 1 2 1 2 1 2 2 2 2 2 0 > , TABLE 3: tests on variances of normal distributions H 0 H 1 test statistic criteria for rejection σσ 2 0 2 = 2 0 2 X ns 0 2 2 0 2 1 = () σ ΧΧ 0 2 21 2 0 2 121 2 >< −− αα ,, or 2 0 2 < 0 2 2 < ,n 2 0 2 > 0 2 2 > ,n 1 2 2 2 = 2 0 2 F s s 0 1 2 2 2 = FF 0 211 01211 > < or 1 2 2 2 < F s s 0 2 2 1 2 = 1 > 1 2 2 2 > F s s 0 1 2 2 2 = 1 > This is a lot to take in at once, but these tables are best learned through use and not study. In this workshop, you will carry out a typical case study, using your own tests constructed on a
CHEN 3010 Workshop #20 Page 3 spreadsheet, and, then you will compare these to tests carried out automatically using Excel’s Data Analysis package. In this way, you will appreciate what’s behind the built-in tests and be able to interpret their results properly. Case Study: Tensile Strength of Roof Coatings An experimental study has been conducted to compare the tensile strength of two types of roof coatings, one based on butyl and the other based on acrylic polymers. A claim has been made that the butyl coatings are stronger. The experimental data are presented in the table below: Tensile Strength (psi) Butyl Acrylic 340.7 263.4 272.6 271.4 246.3 247.7 287.5 248.3 270.1 341.6 332.6 303.9 255.0

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## This note was uploaded on 10/11/2011 for the course CHEN 3010 taught by Professor Kompala,dh during the Spring '08 term at Colorado.

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Workshop20 - CHEN 3010 Applied Data Analysis Names: Fall...

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