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### Course: AP®︎/College Statistics>Unit 12

Lesson 2: Chi square tests for relationships (homogeneity or independence)

# Test statistic and P-value in chi-square tests with two-way tables

You might need: Calculator,Chi-squared table

## Problem

A researcher wanted to see if different breeds of dogs preferred toys of certain colors. The researcher presented each dog with $3$ toys, identical except that each was a different color, and recorded which toy the dog played with the most in a set time period. Here are the outcomes and partial results of a chi-square test (expected counts appear below observed counts):
Chi-square test: Breed vs. toy color
YellowPurpleBlackTotal
Beagle$16$$30$$14$$60$
$24$$23$$13$
Collie$27$$23$$10$$60$
$24$$23$$13$
Husky$29$$16$$15$$60$
$24$$23$$13$
Total$72$$69$$39$$180$
They want to use these results to carry out a ${\chi }^{2}$ test for homogeneity. Assume that all conditions for inference were met.
What are the values of the test statistic and P-value for their test?