Final answer:
The correct conclusion when the F-test statistic is greater than the critical F-score for ANOVA is to reject the null hypothesis. This decision suggests that at least one group mean is significantly different from the others.
option c is the correct
Step-by-step explanation:
When the F-test statistic is greater than the critical F-score for ANOVA (Analysis of Variance), the correct conclusion is to reject the null hypothesis. This decision is made because the null hypothesis posits that there is no difference between the group means, and a higher F-test statistic indicates that the observed differences are too significant to have occurred purely by chance.
By rejecting the null hypothesis, you are acknowledging the likelihood that the differences in means are not due to randomness, thus implying that at least one group mean is significantly different.
In essence, a critical F-score sets the threshold for significance, and if your F-test statistic exceeds this threshold, it indicates that the results are significant at a pre-determined confidence level (typically ). An example would be an experiment where the F statistic is calculated to be 3.67 with k = 3 groups and n = 50 total observations. If the critical F-score at an alpha level of 0.05 is less than 3.67, then we would reject the null hypothesis, suggesting there is a statistically significant difference among the group means.