One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 17 with a sample mean of 203 pounds and a sample standard deviation of 11.8 pounds. You can assume that all of the assumptions are met. Assume that the distribution of the weights is normal. Please use 4 decimal places for all critical values. Required:
a. Find the 95% confidence interval for the true mean weight of the players from the Detroit Red Wings.
b. Calculate the 95% lower bound of the true mean weight of the players from the Detroit Red Wings. Please interpret your result.
c. Why is the lower limit from part b) different from the lower bound in part a)? Please explain your answer by listing the symbols that are different between parts a) and b) and explain why the symbols are used.
d. The 95% confidence interval of the weights for the Boston Bruins is (194.16, 205.81). If the true mean weights for the two teams are different, then it is likely that there will be a more physical game when the two teams meet. Is there any evidence to suggest that the true mean player weight of Detroit is different from that of Boston?