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?
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 the differences in mean scores across the three sleep conditions are not statistically significant, leading to the conclusion that none of the mean scores are significantly different.
This choice implies that there is a specific significant difference among the mean scores. However, the p-value of 0.018, being greater than the significance level of 0.01, indicates that there are no significant differences at all. Therefore, this statement is not supported by the data.
This is the correct choice because the p-value exceeds the significance level, indicating that the differences in mean scores among the sleep conditions are not statistically significant. Thus, there is no evidence to suggest that any of the conditions differ from one another in terms of memory test performance.
This choice suggests that at least one pair of conditions shows a significant difference in mean scores. Given the p-value of 0.018 is greater than the critical value of 0.01, this statement is incorrect as it contradicts the results of the ANOVA test.
This option suggests that every pair of conditions has a significant difference, which is not the case. The p-value indicates that the overall differences are not significant, meaning that it cannot be concluded that there are significant differences between all pairs.
In conclusion, the analysis indicates that none of the mean scores from the memory tests under different sleep conditions show statistically significant differences at the 0.01 significance level. The p-value of 0.018 confirms the lack of significant differences, leading to the conclusion that all conditions yield similar outcomes in terms of memory performance.
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