Question

The blue catfish (Ictalurus Furcatus) is the largest species of North American catfish. The current world record stands at 143 pounds, which was caught in the John H. Kerr Reservoir (Bugg's Island Lake) located in Virginia. According to American Expedition, 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. A sample of 38 blue catfish caught at this reservoir provided a mean of 40.87 with a standard deviation of 4.16. Using a 0.05 significance level, test the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.

Calculate your p-value. Write the result below, and be sure to round your final answer to 4 decimal places.

What is the decision?

• We reject the null hypothesis, since the p-value is less than the significance level.
• We reject the null hypothesis, since the p-value is not less than the significance level.
• We fail to reject the null hypothesis, since the p-value is less than the significance level.
• We fail to reject the null hypothesis, since the p-value is not less than the significance level.

Answer 1

H0: 40

Ha: > 40

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 40.87 - 40) / (4.16 / sqrt(38) )

= 1.29

From T table,

With test statistics of 1.29 and df of 37,

p-value ( right tailed) = 0.1028

We fail to reject the null hypothesis, since the p-value is not less than the significance level.