# EX 31.1 - STAT 400 Examples for Fall 2011 Pearson's 2 Test...

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STAT 400 Examples for 11/29/2011 Fall 2011 Pearson’s χ 2 Test for Goodness of Fit ( Based on Large n ) A random sample of size n is classified into k categories or cells. Let Y 1 , Y 2 , … , Y k denote the respective cell frequencies. n k i i = = 1 Y . Denote the cell probabilities by p 1 , p 2 , … , p k . H 0 : p 1 = p 01 , p 2 = p 02 , , p k = p 0 k . 1 1 0 = = k i i p . 1 2 k Total Observed frequency O Y 1 Y 2 Y k n Probability under H 0 p 01 p 02 p 0 k 1 Expected frequency E under H 0 n p 01 n p 02 n p 0 k n Test Statistic: ( ) ( ) ( ) - = - = - = = = - cells k i i i i k i i i i k p n p n E E O E E O 2 1 2 1 0 2 0 1 Y Q Rejection Region: Reject H 0 if Q k – 1 2 α χ , d.f. = k – 1 = (number of cells) – 1 Pearson’s χ 2 test is an approximate test that is valid only for large samples. As a rule of thumb, n should be large enough so that expected frequency of each cell is at least 5.

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## This note was uploaded on 02/15/2012 for the course STAT 400 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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EX 31.1 - STAT 400 Examples for Fall 2011 Pearson's 2 Test...

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