Mario wondered if students who graduate from a nearby college with an engineering degree have higher yearly salaries, on average, than students graduating with a degree in mathematics. To investigate, he randomly selected ten engineering graduates and eight mathematics graduates. He calculated the mean yearly salary to be $58,421 for the ten engineering graduates and $58,402 for the eight mathematics students. The difference in the sample means of $19 per year resulted in a p-value of 0.478. Based on this information, which of the following statements is correct?
(A) The difference in means is both statistically significant and practically significant.
(B) The difference in means is neither statistically significant nor practically significant.
(C) The difference in means is practically significant, but not statistically significant.
(D) The difference in means is statistically significant, but not practically significant.
This question covers an important topic that is not explicitly covered in the Common Core State Standards. At the advanced level of the GAISE Framework, students should be able to understand what p¬-values represent how to interpret them. Knowing that just because a result is statistically significant does not mean that it is practically significant is a key aspect of understanding p¬-values. Practical significance is grounded in the question’s specific context and can require students to use background knowledge and judgment.
There are two parts to this question: determining if the result is statistically significant and determining if the result is practically significant. Using any reasonable alpha-level (e.g. 0.05 or 0.10), a p-value of 0.478 is not evidence of statistical significance. Given that the values being compared are salaries and the difference between them is only $19, there is little evidence of practical significance for this result. Considering that the difference in salaries is less than three orders of magnitude smaller than the salaries in question, it is unlikely that a reasonable person would choose a major in engineering over a major in mathematics because of the additional $19 per year on average. Option (B) is the only answer choice reflecting that the difference is neither statistically significant nor practically significant.