Which of the following would increase the width of a confidence interval?
Changing from a 99% to 95% confidence level.
Increasing the variability of the outcome.
Increasing the sample size.
Removing an outlier from the data
If you don't know the right alternative, possibly you could find it by eliminating the false alternatives.
Increased variability
Increasing the variability of the outcome.
Increasing the variability of the outcome, increasing the sample size, and removing an outlier from the data would all increase the width of a confidence interval.
To determine which of the following factors would increase the width of a confidence interval, let's analyze each option individually:
1. Changing from a 99% to 95% confidence level: The confidence level represents the certainty that the interval contains the true population parameter. A higher confidence level will result in a wider interval because it requires a larger range of values to encompass that level of certainty. Therefore, changing from a 99% to 95% confidence level would decrease the width of the confidence interval, not increase it.
2. Increasing the variability of the outcome: Variability refers to the spread or dispersion of the data. When the variability of the outcome increases, it means that the data points are more scattered, resulting in an increased range of possible values. Consequently, increasing the variability of the outcome would indeed increase the width of the confidence interval.
3. Increasing the sample size: The sample size is the number of observations or measurements taken. A larger sample size provides more information about the population and leads to a more accurate estimation of the parameter. With an increased sample size, the standard error (a measure of uncertainty) decreases, resulting in a narrower confidence interval. Therefore, increasing the sample size would decrease the width of the confidence interval, not increase it.
4. Removing an outlier from the data: An outlier is a data point that significantly deviates from the other data points. Outliers can have a strong influence on statistical analyses and may artificially widen the confidence interval. By removing an outlier, the range of possible values would decrease, leading to a narrower confidence interval.
Considering the above explanations, the correct answer is 2. Increasing the variability of the outcome would increase the width of a confidence interval.