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?
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 no significant difference among the mean scores across the three sleep conditions. This means that the null hypothesis, which states that all group means are equal, cannot be rejected.
This choice is correct because the F-statistic calculated (0.381) is lower than the critical F-value (0.648). This finding suggests that the differences in memory test performances between the groups are not statistically significant, supporting the conclusion that the mean scores are similar across the different sleep conditions.
This choice is incorrect because the data analysis showed an F-statistic that did not exceed the critical F-value. Therefore, it cannot be concluded that at least one pair of mean scores is significantly different; instead, all means appear to be statistically similar.
This choice is also incorrect. The analysis does not indicate that there are significant differences between all pairs of means. Instead, the results suggest that the means are not significantly different from one another, contradicting the assertion made in this option.
This option is incorrect as well. The F-statistic does not support the notion that any specific pair of mean scores is significantly different. The analysis shows no significant differences at all among the groups.
In conclusion, the results of the one-way ANOVA indicate no significant differences among the mean memory test scores for participants based on the three different sleep conditions. Since the calculated F-statistic is less than the critical value, this confirms that all group means are statistically equivalent, validating choice A as the correct conclusion.
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