Name that Chi-SquareTest

For each question, state whether you would use a goodness of fit test, a test of homogeneity, a test of association/ independence or some other statistical test. Give the degrees of freedom for chi-square tests.

A brokerage firm wants to see whether the type of account a customer has (Silver, Gold, or Platinum) affects the type of trades that customer makes (in person, by phone, or on the Internet). It collects a random sample of 100 trades made by its customers over the past year.

Chi-square test of association/independence 4 degrees of freedom

The brokerage firm also wants to see if the type of account (Silver, Gold, or Platinum) affects the amount of money (in dollars) that the customers invest. It performs a test to see if the mean investment is the same for all three account types.

Not a chi-square test because the amount of money invested is a quantitative variable. We could do three 2-sample tests for means or ANOVA

A car manufacturer wants to know if the quality of a car is affected by what month it was built. They collect an SRS of 500 warranty claims filed over the past two years to test whether defects are randomly distributed with month of manufacture.

Goodness of Fit test 11 degrees of freedom

In July 1991 and again in April 2001, the Gallup Poll asked random samples of 1015 adults about their opinions on working parents. Participants were asked which of the following they saw as the ideal family in today’s society: Both parents work full time, One works full time and one part time, One works and the other stays home with the kids, or No opinion.

Chi-square test of homogeneity 3 degrees of freedom

The academic research office of a large college wants to know if the distribution of courses chosen (Humanities, Social Science, or Science) is different for its residential and nonresidential students. It randomly samples 300 residential and 200 nonresidential students.

Chi-square test of homogeneity 2 degrees of freedom

The academic research office of a large college wants to know if the distribution of courses chosen (Humanities, Social Science, or Science) is different for its residential and nonresidential students. It randomly samples 500 students.

Chi-square test of association/independence 2 degrees of freedom

Is there a difference in the country of manufacture of cars driven by students and staff? A random survey of autos parked in the student parking lot and staff parking lot at a large high school are classified as American or foreign manufactured.

Chi-square test of homogeneity 1 degree of freedom Or 2 proportion z-test

A medical researcher wants to know if blood cholesterol level is related to heart disease. He 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.

Not a Chi-square test because cholesterol level is a quantitative variable. We would use a 2-sample t test.

A medical researcher wants to know if blood cholesterol level is related to heart disease. She examines a database of 10,000 patients to test whether the cholesterol level (low, moderate, or high) is related to whether a person has heart disease or not.

Chi-square test of association/independence 2 degrees of freedom