American Theaters knows that a certain hit movie ran an average of 84 days in 8 each city, and the corresponding standard deviation was 10 days. The manager

of the southeasterndistrict was interested in comparing the movie's popularity

in his region with that in all ofAmerican's other theaters. He randomly chose

75 theaters in his region and found that they ran the movie an average of 81.5 days.

(a) State appropriate hypotheses for testing whether there was a significantdifference in the length of the picture's run between theaters in the southeastern district and all of American's other theaters.

(b) At a 1 percent significance level, test these hypotheses