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 # = 19 inches. However, a survey reported that of a random sample of 46 fish caught, the mean length was x = 18.6 inches, with estimated standard deviation s = 3.1 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than # = 19 Inches? Use a = 0.05. LA USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: M > 19 in; Hip = 19 in O Ho: H 19 in O Ho: H = 19 in; Hi k # 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The standard normal, since the sample size is large and o is unknown. The Student's t, since the sample size is large and a Is known. The Student's t, since the sample size is large and o is unknown, The standard normal, since the sample size is large and o is known. What is the value of the sample test statistic? (Round your answer to three decimal places.)