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AP®︎/College Statistics

Course: AP®︎/College Statistics>Unit 12

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

Making conclusions in chi-square tests for two-way tables

Problem

A market researcher was curious about the colors of different types of vehicles. They obtained a random sample of $180$ sedans and a separate random sample of $180$ trucks. Here is a summary of the colors in each sample and the results from a chi-squared test:
Chi-square test: Color vs. type
TrucksSedans
Red$37$$57$
Expected$47.0$$47.0$
Blue$36$$41$
Expected$38.5$$38.5$
Black$77$$48$
Expected$62.5$$62.5$
Other$30$$34$
Expected$32.0$$32.0$
Assume that all conditions for inference were met.
At the $\alpha =0.05$ significance level, what is the most appropriate conclusion to draw from this test?