Question

Nationally, the proportion of red cars on the road is 0.12. A statistically-minded fan of the Philadelphia Phillies (whose team color is red) wonders if Phillies fans are more likely to drive red cars. One day during a home game, he takes an SRS of 210 cars parked at Citizens Bank Park (the Phillies home field) while a game is being played, and counts 35 red cars. (There are 21,000 parking spaces.) Is this convincing evidence that Phillies fans prefer red cars more than the general population?

Answer 1

To determine if Phillies fans have a different preference for red cars compared to the general population, we calculate the test statistic based on the sample proportion of red cars among cars at a Phillies game and compare it against the national proportion using a hypothesis test.

Step-by-step explanation:

To assess if Phillies fans are more likely to drive red cars than the general population, we use a hypothesis test for proportions. Given that the national proportion of red cars is 0.12, we set this as our null hypothesis (p = 0.12). The alternative hypothesis is that the proportion of red cars among Phillies fans is greater than 0.12 (p > 0.12).

To perform the test, we calculate the test statistic using the sample proportion which is 35 out of 210 (35/210 ≈ 0.1667). Assuming the null hypothesis is true, the test statistic follows a standard normal distribution. We can then calculate the p-value corresponding to our test statistic, and if the p-value is less than our chosen level of significance (commonly α = 0.05), this provides evidence against the null hypothesis in favor of the alternative.

If the p-value is low enough to reject the null hypothesis, it suggests that Phillies fans have a higher preference for red cars. If the p-value is not low enough, we would not have enough evidence to suggest that Phillies fans have a different preference for red cars than the national average.