Questions: To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off some number of the lowest values and the highest values. If we want a 82% confidence interval, what percent of values should we chop off at each end?

To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off some number of the lowest values and the highest values. If we want a 82% confidence interval, what percent of values should we chop off at each end?

Transcript text: To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off some number of the lowest values and the highest values. If we want a $82 \%$ confidence interval, what percent of values should we chop off at each end?

Solution

Solution Steps

Step 1: Determine the Confidence Level

To create a confidence interval using percentiles, we start with the desired confidence level, which is given as $ 82\% $. This means that we want to capture $ 82\% $ of the data in the middle of our distribution.

Step 2: Calculate the Remaining Percentage

The remaining percentage of the data that is not included in the confidence interval can be calculated as: \[ 1 - 0.82 = 0.18 \] This $ 18\% $ represents the total percentage of values that we will chop off from both ends of the distribution.

Step 3: Split the Remaining Percentage

Since we are chopping off values from both the lower and upper ends of the distribution, we divide the remaining percentage by $ 2 $: \[ \frac{0.18}{2} = 0.09 \] This indicates that $ 9\% $ of the values will be chopped off from each end of the distribution.

Step 4: Convert to Percentage

To express this in percentage terms, we multiply by $ 100 $: \[ 0.09 \times 100 = 9.00\% \]