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?
None of the mean scores are significantly different.
The F-statistic of 0.218 is less than the critical F-value of 0.598, indicating that there is no statistically significant difference between the memory test performances across the different sleep conditions. Therefore, we accept the null hypothesis, concluding that the means are equal.
This choice suggests that there is a significant difference in one specific comparison among the means. However, since the F-statistic does not exceed the critical F-value, we cannot conclude that even one pair of mean scores is significantly different; therefore, this option is incorrect.
This option implies that at least one of the comparisons among the conditions shows a significant difference. Again, with an F-statistic of 0.218 being lower than the critical F-value, we are unable to support this claim. Thus, this statement does not hold true based on the given results.
This statement accurately reflects the results of the ANOVA test. As the F-statistic is below the critical value, it confirms that we do not have enough evidence to suggest any significant differences among the mean scores of the three sleep conditions.
This option claims that all pairs of means differ significantly from one another, which is not supported by the results. The F-statistic being less than the critical F-value indicates that no pairs of means are significantly different, making this conclusion incorrect.
In summary, the results of the one-way ANOVA indicate that there are no significant differences in memory test performances under the three sleep conditions studied. The F-statistic of 0.218 being lower than the critical F-value of 0.598 leads us to accept the null hypothesis, confirming that none of the mean scores differ significantly.
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