Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous f

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 ? = 19 inches. However, a survey reported that of a random sample of 25 fish caught, the mean length was x =18.3 inches, with 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? Use ? = 0.05. (Use 3 decimal places for the test statistic and the critical value. Use 4 decimal places for the P-value.)

Conclusion

Reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches.    
Fail to reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches.

Explanation / Answer

sample size,n = 25

sample mean,x = 18.3

standard deviation,s = 2.7

assumed population mean,u = 19

alpha,a = 0.05

H0: u = 19

H1: u < 19

test statistic, t = (x-u)/(s/sqrt(n))

test statistic, t = -1.296

critical value = - t(a,n-1) = - t(0.05,24)

critical value = - 1.711

degree of freedom = n-1 = 24

P-value = 0.1036

Since P-value > 0.05, hence H0 can not be rejected

Fail to reject the null hypothesis, there is insufficient evidence that the average fish length is less than 19 inches.

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