Pyramid Lake is on the Paiute Indian Reservation in Nevada T

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 = 18.7 inches, with estimated standard deviation s = 3.5 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?

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


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

Solution

H0: mu =19\"

Ha: mu < 19\"

Left tailed hyp test

x bar = 18.7

Mean difference = -0.3

Std error = s/rtn = 3.5/rt46 = 0.516

t statistic=-0.58134

df = 46-1 =45

p value =.28207.

The result is not significant at p < .05.

It is not statistically evident to conclude that the average length of a trout caught in Pyramid Lake is less than = 19 inches at 0.05 level