Answer :
When considering the factors that increase the likelihood of a difference in averages of two samples being meaningful, the features are:
1. Larger margin of error: This actually decreases the precision of the estimate. A larger margin of error means that the confidence interval around the sample mean is wider, making it less likely that the observed difference is statistically significant. Therefore, it does not increase the likelihood of the difference being meaningful.
2. Larger samples: Larger sample sizes increase the chances of detecting a true difference if one exists. This is because larger samples provide more information and thus reduce the standard error of the mean, making it easier to identify meaningful differences.
3. Larger difference in averages: If there is a larger difference between the averages of the two samples, it is more likely that this difference is statistically significant and meaningful. Small differences are often within the range of random variation, whereas large differences are less likely to be due to chance.
4. Smaller standard deviation: A smaller standard deviation indicates that the data points are closer to the mean, which reduces the variability within each sample. This makes it easier to detect a significant difference between sample means because the data is more consistent and less spread out.
Given these considerations, the correct answer is:
Larger margin of error
1. Larger margin of error: This actually decreases the precision of the estimate. A larger margin of error means that the confidence interval around the sample mean is wider, making it less likely that the observed difference is statistically significant. Therefore, it does not increase the likelihood of the difference being meaningful.
2. Larger samples: Larger sample sizes increase the chances of detecting a true difference if one exists. This is because larger samples provide more information and thus reduce the standard error of the mean, making it easier to identify meaningful differences.
3. Larger difference in averages: If there is a larger difference between the averages of the two samples, it is more likely that this difference is statistically significant and meaningful. Small differences are often within the range of random variation, whereas large differences are less likely to be due to chance.
4. Smaller standard deviation: A smaller standard deviation indicates that the data points are closer to the mean, which reduces the variability within each sample. This makes it easier to detect a significant difference between sample means because the data is more consistent and less spread out.
Given these considerations, the correct answer is:
Larger margin of error
