Test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value, conclusion about the null hypothesis, and final conclusion that addressess the original claim.
In a recent New York City marathon, 25,221 men finished and 253 dropped out. Also, 12,883 women finished and 163 dropped out (based on data from the New York Times). We want to use a 0.01 significance level to test the claim that the rate of those who finished is the same for men and women.
a. Test the claim using a hypothesis test.
b. Test the claim by constructing an appropriate confidence interval.
c. Based on the results, do men and women finish the New York City marathon at the same rate?