Question

The chi-square test statistic is χ2 = 18.68 and the P-value is between 0.0025 and 0.005. What conclusion should the researcher make? Use α = 0.05.

Answer 1

We don't know what the exact p-value is, but we are told that it's as large as 0.005 which is smaller than alpha = 0.05

Since the p-value is smaller than alpha, this means we reject the null hypothesis.

The way you can remember this is "if the p-value is low, then the null must go". By "low", I mean "smaller than alpha".

Recall that the p-value is the probability of observing that specific test statistic, or larger. So the chances of chi-squared being 18.68 or larger is a probability between 0.0025 and 0.005; there's a very small chance of this happening. The p-value is based entirely on the assumption that the null is correct. But if the null is correct, then the chances of landing on this are very small. We have a contradiction that basically leads to us concluding the null must not be the case. It's not 100% guaranteed of course, but it's fairly strong evidence.

In short, the p-value being smaller than alpha = 0.05 means we reject the null.

In order to accept the null, the p-value must be 0.05 or larger.