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2 weeks ago
Car colors According to Ward's Communication, 19% of sports car enthusiasts prefer a red color, 16.2% silver, 14.7% black, 14.1% green, 14% white, and 22% other colors. A sample of 250 cars at a NASCAR raceway revealed 45 red cars, 42 silver cars, 34 black cars, 40 green cars, 39 white cars, and 50 other color cars. Are NASCAR color preferences typical of sports car enthusiasts? Test an appropriate hypothesis and state your conclusion.
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Stats: Modeling the World


Edition: 4th
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2 weeks ago
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H0: The distribution of the colors of cars at a NASCAR raceway is the same as the distribution of colors preferred by sports car enthusiasts.
HA: The distribution of the colors of cars at a NASCAR raceway is different than the distribution of colors preferred by sports car enthusiasts.
* Counted data condition: We have counts of cars in 6 color categories.
* Randomization Condition: We have a random sample of cars at a NASCAR raceway.
* Expected cell frequency condition: The expected counts are below. These expected values are all at least 5, so the condition is satisfied.

Under these conditions, the sampling distribution of the test statistic is χ2 with 6 - 1 = 5 degrees of freedom.We will do a chi-square goodness-of-fit test.
χ2 = = + ... + = 1.945

P = P2 > 1.945) = 0.8567
The P-value of 0.8567 is high, so we fail to reject the null hypothesis. There is no evidence that color preferences of cars at the NASCAR raceways differ from color preferences of sports car enthusiasts.
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