46. A completely randomized design is used to compare memory test performances... under three conditions: 8 hours of sleep, 6 hours of sleep, and 4 hours of sleep... The results of a one-way ANOVA provide an F-statistic of 0.218 and a critical F-value of 0.598. Which conclusion is appropriate for these results?
Answer: C
None of the mean scores are significantly different.
The results indicate that there is no significant difference among the mean scores for the three sleep conditions, as the F-statistic of 0.218 is less than the critical F-value of 0.598.
A) Exactly one pair of mean scores has a significant difference.
This option is incorrect because the F-statistic provided does not indicate any significant differences between the mean scores. A significant difference would require the F-statistic to be greater than the critical F-value.
B) At least one pairing of mean scores has a significant difference.
This option is also incorrect as the analysis shows that the F-statistic of 0.218 does not exceed the critical F-value of 0.598, indicating that no significant differences can be inferred.
C) None of the mean scores are significantly different.
This option is correct. The F-statistic of 0.218 being lower than the critical value of 0.598 suggests that there are no significant differences between the mean scores of the different sleep conditions tested.
D) There is a significant difference between all pairs of mean scores.
This option is incorrect since the results indicate that there is not a significant difference among the mean scores. If there were significant differences among all pairs, the F-statistic would have to be greater than the critical value.
Conclusion
The conclusion drawn from the ANOVA results is that none of the mean scores for the different sleep conditions show significant differences, as indicated by the F-statistic being less than the critical value. All other options incorrectly suggest the presence of significant differences that the statistical analysis does not support.