## Related questions with answers

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 a random sample of 210 cars parked at Citizens Bank Park (the Phillies home field) and counts 35 red cars. Explain why there is some evidence for the alternative hypothesis.

Solution

VerifiedGiven:

$\begin{align*} x&=\text{Number of successes}=35 \\ n&=\text{Sample size}=210 \end{align*}$

Given claim: proportion is greater than 0.12.

The claim is either the null hypothesis or the alternative hypothesis. The null hypothesis states that the population proportion is equal to the value mentioned in the claim. If the null hypothesis is the claim, then the alternative hypothesis states the opposite of the null hypothesis.

$\begin{align*} H_0&:p=0.12 \\ H_a&:p>0.12 \end{align*}$

The sample proportion is the number of successes divided by the sample size:

$\hat{p}=\dfrac{x}{n}=\dfrac{35}{210}=\dfrac{1}{6}\approx 0.1667$

There is some evidence for the alternative hypothesis, because the sample proportion of 0.1667 is greater than 0.12 and this corresponds with the claim of the alternative hypothesis that the proportion is greater than 0.12.

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