A test to see if U.S. cardinals are significantly younger than cardinals worldwide produces a P-value that is considerably greater than 0.05. Based on this result, statistics students are asked to reach a conclusion about the mean age of U.S. cardinals compared to that of cardinals worldwide. Whose answer is best?

Adam: If the P-value is not small then there must be a large difference. We’ve proven that U.S. cardinals are younger.

Brittany: You can’t say we’ve proven them to be younger, but you can say we have evidence that they’re younger.

Carlos: If the P-value is not small, then the difference we observed is not so improbable if U.S. cardinals were the same age as cardinals worldwide. So we’ve proven that U.S. cardinals are the same age as cardinals worldwide.

Dominique: The P-value is not small, so we failed to produce evidence that U.S. cardinals are significantly younger. That’s not the same thing as proving them to be the same age.