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 (buggs 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. use the data below, which represents the summary statistics for 45 blue catfish caught at this reservoir, and a 0.001 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 = 45; 𝑥̅ = 40.71 pounds; s = 5.05 pounds

a. what type of test will be used in this problem? select an answer

b. identify the null and alternative hypotheses?

h₀: select an answer ?

hₐ: select an answer ?

c. is the original claim located in the null or alternative hypothesis? select an answer

Explanation:

Step1: Determine test type

Since the population standard - deviation is unknown and we are testing a claim about the population mean, a one - sample t - test will be used.

Step2: Formulate hypotheses

The null hypothesis \(H_0\) is a statement of no effect or equality. The alternative hypothesis \(H_a\) is the claim we are trying to find evidence for. The null hypothesis is \(H_0:\mu\leq40\) (where \(\mu\) is the population mean weight of fish in the reservoir) and the alternative hypothesis is \(H_a:\mu > 40\).

Step3: Locate the claim

The original claim is that the mean weight of the fish in the John H. Kerr Reservoir is greater than 40 pounds. This is the alternative hypothesis.

Answer:

a. One - sample t - test
b. \(H_0:\mu\leq40\), \(H_a:\mu > 40\)
c. Alternative hypothesis