Fran is training for her first marathon, and she wants to know if there is a significant difference between the mean number of miles run each week by group runners and individual runners who are training for marathons. She interviews 38 randomly selected people who train in groups, and finds that they run a mean of 49.5 miles per week. Assume that the population standard deviation for group runners is known to be 1.1 miles per week. She also interviews a random sample of 33 people who train on their own and finds that they run a mean of 48.5 miles per week. Assume that the population standard deviation for people who run by themselves is 2.6 miles per week. Test the claim at the 0.01 level of significance. Let group runners training for marathons be Population 1 and let individual runners training for marathons be Population 2. Required:
Draw a conclusion and interpret the decision.