statistics math

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 tr 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, wit estimated standard deviation s = 2.7 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than # = 19 inches? a = 0.05. LA USE SALT (a) What is the level of significance? State the null and alternate hypotheses. O Ho: M = 19 in; H,: M > 19 in O Ho: M = 19 in; H1: # # 19 in O Ho: M = 19 in; H1: # 19 in; H1: M = 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 known. The standard normal, since the sample size is large and o is unknown. The Student's t, since the sample size is large and o is unknown. The Student's t, 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.) (c) Estimate the P-value. O P-value > 0.010 O 0.0010