Question: Fishing: Trout

Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you that the average length of trout caught in Pyramid Lake is \[\mu \] = 19 inches. However, the Creel Survey (published by the Pyramid Lake Paiute Tribe Fisheries Association) reported that for a random sample of 51 fish caught, the mean length was \[\bar{X}\] = 15.5 inches with estimated standard deviation s = 3.2 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than \[\mu \] = 19 inches. Use x = 0.05.