Final answer:
The researcher should reject the null hypothesis due to the p-value of .002 being lower than the alpha of .05. Additional tests like the Tukey test may follow if specific comparisons are needed between groups.
Step-by-step explanation:
When a researcher conducts an F-test and obtains a p-value of .002 with an alpha level set at .05, the decision should be to reject the null hypothesis. The p-value being .002 is much lower than the alpha level of .05, indicating that the results are statistically significant and that there is sufficient evidence against the null hypothesis. In most cases, rejecting the null hypothesis would be enough. However, depending on the study design and the need for post-hoc analysis, a Tukey test might be conducted if the F-test was part of an ANOVA with multiple comparisons to find out which specific groups differ from each other. A t-test for each pair of means would be unnecessary if a Tukey test is planned, as the Tukey test is designed to compare all possible pairs of means while controlling for the Type I error rate.