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?

Solution Steps

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.

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.

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.

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

Final Answer