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 = 2.6 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 alternate hypotheses.

H₀: = 19 in; H₁: 19 in

H₀: < 19 in; H₁: = 19 in

H₀: = 19 in; H₁: < 19 in

H₀: > 19 in; H₁: = 19 in

H₀: = 19 in; H₁: > 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 is known.

The Student's t, since the sample size is large and is unknown.

The standard normal, since the sample size is large and is unknown.

The standard normal, since the sample size is large and is known.