Question

A study has been conducted and the F-statistic for the analysis is reported as 2.395, where the critical F value is 2.400. What is the correct statistical decision?

a. Fail to accept the alternative hypothesis.
b. Fail to reject the null hypothesis.
c. Reject the null hypothesis.
d. Accept the alternative hypothesis.

Answer 1

The correct decision is (b) to "Fail to reject the null hypothesis" since the reported F-statistic (2.395) is below the critical F value (2.400).

The statistical decision is (b) "Fail to reject the null hypothesis" as the reported F-statistic (2.395) is marginally below the critical F value (2.400).

This implies insufficient evidence to reject the null hypothesis, suggesting that observed differences are likely due to random variation. While the result is not statistically significant, careful consideration of practical significance and context is crucial.

The decision underscores the importance of weighing statistical findings against the chosen significance level and recognizing the limitations of hypothesis testing. Further exploration or larger sample sizes may be needed to draw more definitive conclusions in future analyses.