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Chapter 3: Problem 89

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 our bootstrap distribution contains values for 1000 bootstrap samples, indicate how many we chop off at each end for each confidence level given. (a) \(95 \%\) (b) \(90 \%\) (c) \(98 \%\) (d) \(99 \%\)

Short Answer

Expert verified
For the \(95 \%\) confidence level, we chop off 25 samples from each end. For the \(90 \%\) confidence level, we chop off 50 samples from each end. For the \(98 \%\) confidence level, we chop off 10 samples from each end. And for the \(99 \%\) confidence level, we chop off 5 samples from each end.

Step by step solution

01

Understanding Confidence Interval

Confidence interval in a bootstrap distribution is determined by the percentiles. For instance, for a \(95 \%\) confidence interval in a case of 1000 bootstrap samples, we keep the middle \(95 \%\) and exclude \(5 \%\) of the values, these are equally divided and are excluded from both ends which are usually the lowest and the highest values. Hence, calculating it, we have \(1000 \times ((100-95) / 100)/2\). This is calculated as such because we are removing \(5 \%\) entirely, thus, the half on each side.
02

Calculating for (a) \(95 \%\) confidence level

Computing for a \(95 \%\) confidence interval, we do: \(1000 \times (5 / 100)/2 = 25\). Thus, we chop off 25 bootstrap samples from each end.
03

Calculating for (b) \(90 \%\) confidence level

Computing for a \(90 \%\) confidence interval, we do: \(1000 \times (10 / 100)/2 = 50\). Thus, we chop off 50 bootstrap samples from each end.
04

Calculating for (c) \(98 \%\) confidence level

Computing for a \(98 \%\) confidence interval, we do: \(1000 \times (2 / 100)/2 = 10\). Thus, we chop off 10 bootstrap samples from each end.
05

Calculating for (d) \(99 \%\) confidence level

Computing for a \(99 \%\) confidence interval, we do: \(1000 \times (1 / 100)/2 = 5\). Thus, we chop off 5 bootstrap samples from each end.

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Most popular questions from this chapter

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