Question

If the actual distribution of tusk lengths does not match the ones predicted with the H-W equation, it may indicate that natural selection is acting on this population and causing the most beneficial phenotype to increase in abundance. To determine whether or not this is true the scientists perform a statistical test. This test results in a p-value of 0.021. What does this mean?

Answer 1

See explanation below

Explanation:

It depends on what null hypothesis is under consideration.

One of the most common null hypothesis that are subject of study in a given statistical model is the mean predicted by the model.

In this case, the scientist probably observed that the mean of tusk lengths she obtained in a sample did not match the one predicted with the H-W equation.

So, she decided to perform a statistical study by collecting random samples and measuring the tusk lengths to determine a new possible mean and contrast it against the one predicted by the H-W equation.

Let's call M the mean predicted by the H-W equation, and S the mean obtained by the scientist.

If M different of S and the p-value is 0.021, that means that there is at most 2.1% of probability that the difference between M and S could be due to a random sampling error.

It should be kept in mind that the p-value does not represent the probability that the scientist is wrong.