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**X2 Goodness of Fit X2 Test for Homogeneity X2 Test for Independence**

Which test to use? X2 Goodness of Fit X2 Test for Homogeneity X2 Test for Independence

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**Chi-squared independence (one sample – 2 variables)**

A brokerage firm wants to see whether the type of account a customer has (Silver, Gold, Platinum) affects the type of trades that a customer makes (in person, by phone, or on the Internet). It collects a random sample of trades made for its customers over the past year and performs a test. Chi-squared independence (one sample – 2 variables)

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**Chi-squared Goodness of Fit**

A brokerage firm wants to see whether the type of account a customer has (Silver, Gold, Platinum) affects the type of trades that a customer makes (in person, by phone, or on the Internet). It collects a random sample of trades made for its customers over the past year and performs a test. That brokerage firm also wants to know if the type of account affects the size of the account (in dollars). It performs a test to see if the mean size of the account is the same for the three account types. Chi-squared Goodness of Fit

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**Chi squared – homogeneity**

The academic research office at a large community college wants to see whether the distribution of courses chosen (Humanities, Social Science, or Science) is different for its residential and nonresidential students. It assembles last semester’s data and performs a test. Chi squared – homogeneity (one variable 2 groups)

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**Chi squared GOF (existing model)**

Is the quality of a car affected by what day it was built? A car manufacturer examines a random sample of the warranty claims filed over the past two years to test whether defects are randomly distributed across days of the work week. Chi squared GOF (existing model)

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**Chi-squared independence (one sample – 2 variables)**

A medical researcher wants to know if blood cholesterol level is related to heart disease. She examines a database of 10,000 patients, testing whether the cholesterol level (in milligrams) is related to whether a person has heart disease or not. Chi-squared independence (one sample – 2 variables)

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**Chi-squared independence (one sample – 2 variables)**

A student wants to find out whether political leaning (liberal, moderate, or conservative) is related to choice of major. He surveys 500 randomly chosen students and performs a test. Chi-squared independence (one sample – 2 variables)

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**Difference of proportions**

Among randomly selected pets, 27% of the 188 dogs and 18%of the 167 cats had fleas. Does this indicate a significant difference in rates of flea problems for these two pets? Difference of proportions (two samples)

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**(two independent samples)**

A supermarket chain wants to know which of two merchandise display methods is more effective. They randomly assign 15 stores to use display type A and 15 others to use display type B, then collect data about the number of items sold at each store. Difference of means (two independent samples)

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**Are there more broken bones in summer or winter**

Are there more broken bones in summer or winter? We get records about the number of fractures treated in January and July at a random sample of 25 emergency rooms. Mean of differences (matched pairs)

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