Pyramid Lake is on the Paiute Indian Reservation in Nevada. The lake is famous f
ID: 1767550 • Letter: P
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
Test statistic:Critical Value:
P- Value:
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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