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 the 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 35 blue catfish caught at this reservoir provided a mean of 40.36 with a standard deviation of 2.41. 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.

a) Identify the null and alternative hypotheses?

Ho:______, _______

H1: _____, _______

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 3 decimal places. ______

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

f) What is the decision?

• a) We reject the null hypothesis, since the p-value is less than the significance level.

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

• c) We fail to reject the null hypothesis, since the p-value is less than the significance level.

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

g) Select the correct conclusion.

• a)There is sufficient evidence to conclude that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds.

• b) There is not sufficient evidence to conclude that the mean weight of the fish in the John H. c) Kerr Reservoir is greater than 40 pounds.

• d) There is sufficient evidence to conclude that the mean weight of the fish in the John H.

• e) Kerr Reservoir is 40 pounds.

• f) There is not sufficient evidence to conclude that the mean weight of the fish in the John H. g) Kerr Reservoir is 40 pounds.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 40
Alternative Hypothesis: μ > 40

b)

This is right tailed test,

c)

for α = 0.05

d)

t = (xbar - mu)/(s/sqrt(n))
t = (40.36 - 40)/(2.41/sqrt(35))
t = 0.884

e)

P-value Approach
P-value = 0.1915

f)

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

g)

b) There is not sufficient evidence to conclude that the mean weight of the fish in the John H. c) Kerr Reservoir is greater than 40 pounds.