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Chapter 15

OMIS 2010 Chapter Notes - Chapter 15: Null Hypothesis, Standard Deviation, Contingency Table

Operations Management and Information System
Course Code
OMIS 2010
Alan Marshall

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Chapter 15: Chi-Squared Tests
Chi-Squared Goodness-of-Fit Test
-Applied to multinomial experiment; generalization of a binomial experiment
-In multinomial experiment: there are two or more possible outcomes per trial
Multinomial Experiment
1) Experiment consists of fixed number of “n” trials
2) Outcome of each trail can be classified into one of “k” categories called cells
3) Probability of pi, that the outcome will fall into cell I remains constant for each trial (p1+p2+…pk = 1)
4) Each trial of experiment is independent of other trials
-We obtain set of observed frequencies f1, f2…, fk where fi is observed frequency of outcomes falling into
cell I, for I = 1, 2, …. K
-Use observed frequencies to draw inferences about cell probabilities
-Expected frequency: ei = n x (pi)
-If observed and expected frequencies are different, we conclude that null hypothesis is false
-Goodness of fit test: measures similarity of expected and observed frequencies
-Sampling distribution is approx.. chi squared with V = k – 1, degrees of freedom
-Small test statistic supports null hypothesis
Required condition
-Actual sampling distribution of test statistic defined is discrete, but it can be approximated if sample size
is large
Rule of 5
oSample size must be large enough so that expected value for each cell must be 5 or more
oWhen necessary, cells should be combined to satisfy this condition
Factors that identify chi-squared goodness of fit test
-Describe a single population, nominal data, 2 or more categories
Chi-Squared Test of Contingency Table
-Use data in a table to see whether two classifications of a population of nominal data are statistically
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