Question

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 μ = 19inches. However, a survey reported that of a random sample of 15 fish caught, the mean length was x = 18.0 inches, with estimated standard deviation s = 3.3 inches. Do these data indicate that the average length of a trout caught in Pyramid Lake is less than μ = 19 inches? Use α = 0.01 (thee decimal places for test statistic. four for the p value).

A) What is the value of the sample test statistic? (Round your answer to three decimal places.)


B) Find the P-value. (Round your answer to four decimal places.)

C. What is the critical value (3 decimal places)

D. reject null, there is sufficient evidence. reject null, there is insufficient evidence. fail to reject null, there is sufficient evidence. fail to reject null, there is insufficient evidence.

Answer 1

a)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (18 - 19)/(3.3/sqrt(15))
t = -1.174

b)

P-value Approach
P-value = 0.1300

c)

Critical value of t is -2.624.

d)
fail to reject null, there is insufficient evidence.

As P-value >= 0.01, fail to reject null hypothesis.