Final Answer:
The statement that is NOT correct is 3) The ANOVA results will be the same.
Step-by-step explanation:
When conducting an Analysis of Variance (ANOVA), the within-group variability decreasing and the sample sizes increasing can significantly impact the results. Increasing sample sizes by a factor of 10 generally improves the precision of estimates and makes the results more reliable. The reduction in within-group variability further enhances the accuracy of the analysis by potentially increasing the F-statistic, which measures the difference between group means relative to within-group variability. Thus, the results of the ANOVA are likely to differ due to these changes in sample size and within-group variability.
Mathematically, the F-statistic in ANOVA is calculated as F = between-group variability / within-group variability. Increasing the sample size by a factor of 10 reduces the within-group variability, causing the denominator of the F-statistic to decrease. Consequently, the F-value is likely to increase. With a significant increase in the F-value, the results of the ANOVA are expected to differ between the preliminary sample and the additional data due to the altered variability and sample sizes.
Therefore, the assumption that the ANOVA results will remain the same with the increased sample size and reduced within-group variability is incorrect. These changes are expected to influence the F-value and subsequently affect the statistical significance and conclusions drawn from the analysis, indicating that the statement "The ANOVA results will be the same" is not accurate in this scenario. correct is 3) The ANOVA results will be the same.