American Theaters knows that a certain hit movie ran an average () of 84 days in each city, and the corresponding standard deviation () was 10 days.The manager of the southeastern district was interested in comparing the movie's popularity in his region with that in all of American's other theaters.He randomly chose 75 theaters in his region and found that they ran the movie an average (x) of 81.5 days.At the 0.01 significance level, can the manager conclude that there was a significant difference in the length of the picture's run between theaters in the southeastern district and all of American's other theaters?