Answer:
c) Do not reject the null hypothesis; these fish are not larger than usual.
Explanation:
A particular species of salmon has an average weight of 57 lbs, with a standard deviation of 6.3 lbs. Assuming the weight, X, is normally distributed:

Researchers studying salmon in a particular river find that in a sample of 45 fish, the average weight is 58.5 lbs.
To determine what the researchers should do, we need to perform a hypothesis test to assess whether the sample average weight of 58.5 lbs is significantly different from the population average weight of 57 lbs.
Let μ be the mean weight of salmon (in pounds).
We are testing to see if the mean weight has increased, so this is a one-tailed test. Therefore, the hypotheses are:
- Null hypothesis H₀: μ = 57
- Alternative hypothesis H₁: μ > 57
We have not been given a significance level, so we will assume it is 5%.
Therefore, α = 0.05.

The sample mean
is 58.5 where n = 45.
Therefore, the test statistic is:

This is a one-tailed test and values more likely to occur under H₁ are at the higher end of the distribution. Therefore, we need to find the critical value, z, such that P(Z > z) = 0.05.
Using a calculator, P(Z ≤ z) = 0.95 for z = 1.645.
So the critical region is Z > 1.645.
Since 1.597 < 1.645, the result does not lie in the critical region and is not significant. Therefore, there is insufficient evidence at the 5% level of significance to reject H₀ in favour of the alternative hypothesis that the mean salmon weight has gone up.