04_09 - STAT 410 Examples for 04/09/2008 Spring 2008...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 410 Examples for 04/09/2008 Spring 2008 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 10 , p 2 = p 20 , … , p k = p k 0 . 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 10 p 20 p k 0 1 Expected frequency E under H 0 n p 10 n p 20 n p k 0 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.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
1. The financial manager in charge of accounts receivable department is concerned about
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 02/11/2011 for the course STAT 410 taught by Professor Monrad during the Spring '08 term at University of Illinois, Urbana Champaign.

Page1 / 4

04_09 - STAT 410 Examples for 04/09/2008 Spring 2008...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online