6. [-/4.08 Points] DETAILS BBUNDERSTAT12 8.2.014.MI.S. MY NOTES ASK YOUR TEACHER 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 = 2.5 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. USE SALT (a) What is the level of significance? State the null and alternate hypotheses. Ho: H = 19 in; H1: M $ 19 in Ho: H = 19 in; H1: # > 19 in Ho: H 19 in; H1: p = 19 in (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. The Student's t, since the sample size is large and a 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 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.) c) Estimate the P-value. P-value > 0.010 0.0010