Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous for cutthroat trout. Suppose a friend tells you the that the average length of trout caught in Pyramid Lake is = 19 inches. However, the Creel Survey (published by the Pyramid Lake Paiute Tribe Fisheries Association) reported that of a random sample of 51 fish caught, the mean length was = 18.5 inches, with estimated standard deviation = 3.2 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than = 19 inches? Use = 0.05. a) What is the level of significance? State the null and alternative hypotheses. b) What sampling distribution will you use? How many degrees of freedom will we use (if appropriate)?Explain the rationale for your choice of sampling distribution. c) Compute the appropriate sampling distribution of the sample test statistic. d) Find the critical value. e) Based on your answers in parts (a) through (d), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level ? f) Interpret your conclusion in the context of the application