Question

The blue catfish (Ictalurus Furcatus) is the largest species of North Amercian 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 Amercian 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. Use the data below, which represents the summary statistics for 55 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.

n=55 n=55; x=40.28 x=40.28 pounds; s=2.41 s=2.41 pounds

a) Identify the null and alternative hypotheses?

H0H0: ? p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥  

H1H1: ? p = p ≠ p < p > p ≤ p ≥ μ = μ ≠ μ < μ > μ ≤ μ ≥  

b) What type of hypothesis test should you conduct (left-, right-, or two-tailed)?

• left-tailed
• right-tailed
• two-tailed

c) Identify the appropriate significance level.


d) Calculate your test statistic. Write the result below, and be sure to round your final answer to two decimal places.


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


f) Do you reject the null hypothesis?

• 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.

g) Select the statement below that best represents the conclusion that can be made.

• There is sufficient evidence to warrant rejection of the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.
• There is not sufficient evidence to warrant rejection of the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.
• The sample data support the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.
• There is not sufficient sample evidence to support the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.

Answer 1

Solution :

Given that ,

= 40

= 40.28

s = 2.41

n = 55

The null and alternative hypothesis is ,

H0 :   = 40

Ha : > 40

This is the right tailed test .

Test statistic = T

= ( - ) / s / n

= ( 40.28 - 40 ) / 2.41 / 55

= 0.86

The test statistic = 0.86

df = n - 1 = 55 - 1 = 54

P- value = 1 - ( t 0.86 , 54 )

= 1 - 0.8032

= 0.1968

P-value = 0.1968

= 0.05

0.1968 > 0.05

P-value >

Fail to reject the null hypothesis .

f) Do you reject the null hypothesis

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

Conclusion : - There is not sufficient sample evidence to support the claim that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.