8. A researcher used a one-way classification to compare memory test performances of test participants based on three conditions: 8 hours of sleep, 6 hours of sleep, and 4 hours of sleep. The researcher randomly selected 20 adults for each of the three conditions and then compared the resulting mean scores. A one-way ANOVA provided an F-statistic of 0.381 and a critical F-value of 0.648.What is the appropriate conclusion?
Answer: A
None of the mean scores are significantly different.
The F-statistic of 0.381 is less than the critical F-value of 0.648, indicating that there is not enough evidence to conclude that there are significant differences among the mean scores of participants across the three sleep conditions.
A) None of the mean scores are significantly different.
This option is correct as it accurately reflects the outcome of the one-way ANOVA. Since the calculated F-statistic is lower than the critical F-value, it suggests that the differences in mean scores among the groups are not statistically significant.
B) At least one pairing of mean scores has a significant difference.
This option is incorrect because the results of the ANOVA do not support the conclusion that any pair of mean scores significantly differs from one another. The F-statistic being lower than the critical value indicates no significant differences.
C) There is a significant difference between all pairs of mean scores.
This option is incorrect as the ANOVA results do not support the claim that all pairs of mean scores are significantly different. The F-statistic does not exceed the critical value, which means no significant differences exist among the groups.
D) Exactly one pair of mean scores has a significant difference.
This option is also incorrect. The ANOVA results indicate that no significant differences exist among the mean scores, thus ruling out the possibility of exactly one pair being significantly different.
Conclusion
In conclusion, the correct answer is A, as the statistical analysis demonstrates that none of the mean scores are significantly different due to the F-statistic being below the critical threshold. All other options are incorrect because they imply the existence of significant differences among the groups, which the data does not support.