The p-value associated with an F-statistic of 5.4, with numerator degrees of freedom = 2 and denominator degrees of freedom = 9, is approximately 0.021.
In statistical hypothesis testing, the F-statistic is often used in analysis of variance (ANOVA) to compare variances between groups. The associated p-value helps determine the statistical significance of the F-statistic.
In this context, an F-statistic of 5.4 is given with numerator degrees of freedom (df1 ) equal to 2 and denominator degrees of freedom (df2) equal to 9. The p-value is calculated based on the F-distribution, which depends on both df1 and df2.
The p-value represents the probability of observing an F-statistic as extreme as, or more extreme than, the one obtained, assuming the null hypothesis is true. In this case, a p-value of approximately 0.021 suggests that, under the assumption of no effect (null hypothesis), the observed F-statistic is unlikely to occur by chance.
Researchers typically compare the p-value to a predetermined significance level (often denoted as α, commonly set at 0.05) to decide whether to reject the null hypothesis. In this instance, with a p-value of 0.021, one may choose to reject the null hypothesis in favor of the alternative hypothesis, indicating that there is evidence of a significant difference in variances between the groups.
Complete question:
Find the p-value associated with an F-statistic of 5.4, with numerator degrees of freedom = 2 and denominator degrees of freedom = 9