Cherry Blossom 10-mile and 5K runs ~ Since 1973, the Cherry Blossom 10-Mile Run has been an annual race held in Washington D.C. Elite runners from around the world often use the race as a final warm up for the Boston Marathon, which is typically held two weeks later.Approximately 20,000 runners sign up to participate in the race in each year. Most of the participants compete in the 10-mile race, but for many different reasons a group of the participants elect to run a 5 kilometer (5K) race instead.Ticia is a physical therapist who specializes in sports medicine. She wonders if there is a difference in the mean age of people who run the 10-mile event compared to the people who run the 5K event on the same day.From a random sample of 58 participants who ran the 10-mile race, Ticia calculates a mean age of 38.1 years with a standard deviation of 10.52. Using a random sample of 53 participants who ran the 5K race, she calculates a mean age of 38 years with a standard deviation of 12.46.Round all calculated values in this problem to 4 decimal places.

Assume the conditions for this procedure have been met. What is the appropriate test statistic? ? z t X^2 =

4. What is the p-value using 102.234827 degrees of freedom?p-value =

5. Use the data to construct a 95% confidence interval for the true difference, 1212 using 102.234827 degrees of freedom.( , ).

6. Because all participants must be at least 18 years old, the variable age for each population group of participants cannot be assumed to have a normal distribution. Does knowing this invalidate the results of the t-distribution based inference procedures above? ? Yes No becauseA. All t-distribution procedures require the sample data to be normally distributed. B. Both samples were simple random samples of the population of participants. C. The sample size from each group of participants is more than 30. D. The expected race times for both races are larger than 30 minutes.

Note: You can earn partial credit on this problem.