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; (\bar{x}=40.71) pounds s = 5.05 pounds

a. calculate your test statistic. write the result below, and be sure to round your final answer to two decimal places.
b. calculate your p - value. write the result below, and be sure to round your final answer to four decimal places.

Explanation:

Step1: Identify the formula for the t - test statistic

For a one - sample t - test, the formula is $t=\frac{\bar{x}-\mu}{s/\sqrt{n}}$, where $\bar{x}$ is the sample mean, $\mu$ is the hypothesized population mean, $s$ is the sample standard deviation, and $n$ is the sample size.

Step2: Substitute the given values into the formula

We have $\bar{x} = 40.71$, $\mu = 40$, $s = 5.05$, and $n = 45$.
$t=\frac{40.71 - 40}{5.05/\sqrt{45}}$
$t=\frac{0.71}{5.05/6.7082}$
$t=\frac{0.71}{0.7528}\approx0.94$

Step3: Calculate the degrees of freedom

The degrees of freedom for a one - sample t - test is $df=n - 1$. So, $df=45-1 = 44$.

Step4: Find the p - value

Since this is a right - tailed test, we use the t - distribution table or a calculator (e.g., using a TI - 84 Plus: tcdf(0.94,1E99,44)). The p - value is approximately $0.1762$.

Answer:

a. $0.94$
b. $0.1762$