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
increasing the variability
To determine which of the following options would increase the width of a confidence interval, let's understand what a confidence interval is. A confidence interval is a range of values that provides an estimate of the true population parameter. It is calculated based on a sample taken from the population.
Here are the options presented:
1. Changing from a 99% to 95% confidence level: The confidence level refers to the level of certainty that the true population parameter will fall within the confidence interval. A higher confidence level, such as 99%, means that we are more certain that the true parameter falls within the interval. Conversely, a lower confidence level, such as 95%, indicates less certainty. Changing from a 99% confidence level to a 95% level would decrease the width of the confidence interval, as it includes a smaller range of values and is therefore more precise. Therefore, changing from a 99% to 95% confidence level would not increase the width of the interval.
2. Increasing the variability of the outcome: Variability refers to how spread out the data points are from the mean. If the data points are more dispersed, the variability is higher. Increasing the variability of the outcome would increase the width of the confidence interval since there is more uncertainty regarding the true parameter. So, increasing the variability of the outcome would increase the width of the confidence interval.
3. Increasing the sample size: The larger the sample size, the more representative it is of the population and the more precise the estimate of the true parameter. Increasing the sample size reduces the sampling error and tends to narrow the confidence interval. Therefore, increasing the sample size would decrease the width of the confidence interval.
4. Removing an outlier from the data: An outlier is a data point that significantly deviates from the other data points in the dataset. If an outlier is removed from the data, it can have an impact on the mean and standard deviation, which are used to calculate the confidence interval. Removing an outlier can potentially reduce the variability, which might lead to a narrower confidence interval. Therefore, removing an outlier from the data could decrease the width of the confidence interval.
In summary, increasing the variability of the outcome and removing an outlier from the data would increase the width of the confidence interval, while increasing the sample size and changing from a 99% to 95% confidence level would decrease the width of the interval.