24. In a one-way classification, a researcher compared memory test performances of test participants under three conditions: 8 hours of sleep, 6 hours of sleep, and 4 hours of sleep. The researcher randomly selected eight adults for each of the three conditions and then compared the resulting mean scores. The significance level is ? = 0.01, and a one-way ANOVA provided a p-value of 0.018.What is the appropriate conclusion?
Answer: B
None of the mean scores are significantly different.
The p-value obtained from the one-way ANOVA is 0.018, which is greater than the significance level of 0.01. This indicates that there is not enough evidence to conclude that any of the mean scores from the different sleep conditions are significantly different from one another.
A) Exactly one pair of mean scores has a significant difference.
This option is incorrect because the p-value of 0.018 suggests that there is no significant difference between any pairs of mean scores. A significant difference would require a p-value less than 0.01.
B) None of the mean scores are significantly different.
This option is correct as the p-value of 0.018 exceeds the alpha level of 0.01, indicating that the differences in mean scores among the sleep conditions are not statistically significant.
C) At least one pairing of mean scores has a significant difference.
This option is incorrect because the p-value indicates that there is insufficient evidence to support the claim that at least one pairing of mean scores is significantly different. A significant finding would require a p-value below the significance threshold.
D) There is a significant difference between all pairs of mean scores.
This option is incorrect as well, since the p-value does not support the conclusion that all pairs of mean scores are significantly different. In fact, the results suggest the opposite, highlighting no significant differences.
Conclusion
The correct conclusion is that none of the mean scores are significantly different, as indicated by the p-value of 0.018 being greater than the significance level of 0.01. All other options incorrectly interpret the statistical findings of the one-way ANOVA, suggesting that significant differences exist when, in fact, the data does not support such claims.