Question

Philly fanatics? 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.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameter of interest.

b. Explain why there is some evidence for the alternative hypothesis.

c. The P-value for the test in (a) is 0.0187. Interpret the P-value.

d. What conclusion would you make at the α=0.05 significance level?

Short answer

a. $H_0:p=0.12$and $H_1:p>0.12$

b. Sample proportion is greater than $0.12$and it corresponds to claim of alternative hypothesis.

c. There is a $1.87\%$confidence that $35$or more out of $210$randomly selected Phillies fans own a red car.

d. Enough convincing proof is present that the proportion of red cars among Phillies fans is greater than $0.12$..

Step-by-step solution

Part (a) Step 1: Given Information

It is given that claim is greater than$0.12$.

Part (a) Step 2: Explanation

am