Question

it is known that the trout in carter lake back in 1990 had an average weight of 5 pounds with a standard deviation of 1.4 pounds. it is wondered if the average has increased since 1990. assume the distribution is normal, and that the standard deviation has not changed. a new sample of 25 fish is taken, and the average was 5.672 the following hypothesis was done:

Answer 1

To formally state the hypothesis, we can set up the null and alternative hypotheses as follows:

Null Hypothesis (H₀): The average weight of trout in Carter Lake has not increased since 1990.
Alternative Hypothesis (H₁): The average weight of trout in Carter Lake has increased since 1990.

Symbolically, this can be represented as:

H₀: μ = 5 (The population mean weight is equal to 5 pounds)
H₁: μ > 5 (The population mean weight is greater than 5 pounds)

In this case, since we are testing whether the average weight has increased, it is a one-tailed test with the alternative hypothesis being one-sided (greater than).

To further analyze the hypothesis, we can perform a statistical test, such as a one-sample t-test, using the given information from the new sample of 25 fish. This would involve calculating the test statistic and comparing it to a critical value or finding the corresponding p-value to make a decision regarding the hypothesis.

Please note that without additional information, such as the sample mean weight and the corresponding test statistics, it is not possible to draw any conclusions regarding the hypothesis or determine the significance of the observed increase in the average weight.