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Chapter 3: Problem 88

To create a confidence interval from a bootstrap distribution using percentiles, we keep the middle values and chop off a certain percent from each tail. Indicate what percent of values must be chopped off from each tail for each confidence level given. (a) \(95 \%\) (b) \(90 \%\) (c) \(98 \%\) (d) \(99 \%\)

Short Answer

Expert verified
(a) 2.5%, (b) 5%, (c) 1%, and (d) 0.5%.

Step by step solution

01

Solution for (a)

The confidence level is 95%, indicating that the middle 95% values should be kept, while the remaining 5% should be excluded. These 5% are divided equally at both ends of the distribution. So, 5% / 2 = 2.5% of the values need to be chopped off from each tail.
02

Solution for (b)

The confidence level is 90%, which means that the middle 90% of the values need to be kept, whereas the remaining 10% should be excluded. These 10% are divided equally at both ends of the distribution. Hence, 10% / 2 = 5% of the values need to be chopped off from each tail.
03

Solution for (c)

For a confidence level of 98%, we should keep the middle 98% values and exclude the remaining 2%. As the 2% is divided equally at both ends of the distribution, therefore 2% / 2 = 1% values must be chopped off from each tail.
04

Solution for (d)

For a 99% confidence level, the middle 99% values should be kept, whereas the remaining 1% should be excluded. As the 1% is divided equally at both ends of the distribution, thus 1% / 2 = 0.5% of the values should be chopped off from each tail.

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Most popular questions from this chapter

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