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AP®︎/College Statistics

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

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

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:

χ^{2} = 11.558, DF = 3, P-value = 0.009

Assume that all conditions for inference were met.

At the $α = 0.05$ ‍ significance level, what is the most appropriate conclusion to draw from this test?

(Choice A)
This is convincing evidence that color and type of car are not independent.
(Choice B)
We lack evidence to say that color and type of car are not independent.
(Choice C)
This is convincing evidence that the distribution of color differs between trucks and sedans in this population.
(Choice D)
This isn't enough evidence to say that the distribution of color differs between trucks and sedans in this population.
(Choice E)
Buying certain types of cars causes people to be more likely to choose certain colors.

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