# Audrey is training for her first marathon, and she wants to know if there is a significant difference

Audrey is training for her first marathon, and she wants to know if there is a significant difference between the true mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 55 randomly selected people who train in groups and finds that they run a mean of 46.9 miles per week. Assume that the population standard deviation for the group runners is known to be 5.2 miles per week. She also interviews a random sample of 45 people who train on their own and finds that they run a mean of 49.9 miles per week. Assume that the population standard deviation for people who run by themselves is 5.7
miles per week.

Find the P
-value for the hypothesis test. Round your answer to four decimal places.
b. Is there sufficient evidence to conclude that there is a significant difference between the true mean number of miles run each week by group runners and individual runners who are training for marathons? Test the claim at the 0.01 level of significance.