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Statistics Hypothesis Test: Flat Tire

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A classic tale involves for carpooling students who missed a test and gave as an excuse a flat tire. On the makeup test, the instructor asked the students to identify the particular tire that went flat. If they really didn't have a flat tire, would they be able to identify the same tire? The author asked 41 other students to identify the tire they would select. The results are listed in the following table (except one student who selected the spare). Use a 0.05 significance level to test the author's claim that the results fit a uniform distribution. What does the result suggest about the ability of the four students to select the same tire when they really didn't have a flat?

Tire: Left front Right front Left rear Right rear
Number selected: 11 15 8 6

Conduct the hypothesis test and provide the test statistic, critical value and/or p-value, and state the conclusion.

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Solution Summary

The solution discusses a statistics hypothesis test regarding a flat tire.

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Null hypothesis: the distribution is not different from the uniform distribution.
Alternative hypothesis: the distribution is significantly different from the uniform distribution.

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