Question

The blue catfish is the largest species of North American catfish. The current world record stands at 134 pounds, which was caught in the John H Kerr Reservoir. The average weight of a blue catfish is between 20 to 40 pounds. Given that the largest blue catfish ever caught was at the John H Kerr reservoir, you believe that the mean weight of the fish in this reservoir is greater than 40 pounds. Use the data below which represents the summary statistics for 48 blue catfish caught at this reservoir, and a 0.05 significance level to test the claim that the mean weight of the fish in the John H. Kerr reservoir is greater than 40 pounds. (please dont use a table, use calculator)

n = 48 ; x bar = 40.4 ; s = 2.65

Answer 1

for the given data The Hypotheses are:

Rejection region:

Reject Ho if T> t _{0.05 , 47} =1.68  Where 47 is the degree of freedon. We are using T-distribution here because the Population standard deviation is unknown and also the sample size is greater than 30

Test statistic:

P-value :

P-value computed using T table at 95 % confidence level as

0.1< P-value< 0.25

Conclusion:

Since T < t and P-value > 0.05 hence we fail to reject the null hypothesis and conclude that there insufficient evidence to support the null hypothesis that the mean is greater than 40.

The T-table: