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Bootstrap percentile interval

The main idea in the previous exercise was that the distance between the original sample \(\hat{p}\) and the resampled (or bootstrapped) \(\hat{p}^*\) values gives a measure for how far the original \(\hat{p}\) is from the true population proportion.

The same variability can be measured through a different mechanism. As before, if \(\hat{p}\) is sufficiently close to the true parameter, then the resampled (bootstrapped) \(\hat{p}^*\) values will vary in such a way that they overlap with the true parameter.

Instead of using \(\pm 2 SE\) as a way to measure the middle 95% of the sampled \(\hat{p}\) values, you can find the middle of the resampled \(\hat{p}^*\) values by removing the upper and lower 2.5%. Note that this second method of constructing bootstrap intervals also gives an intuitive way for making 90% or 99% confidence intervals as well as 95% intervals.

The bootstrapped resamples, one_poll_boot, and the proportion of yes votes, p_hat are available in your workspace.

This exercise is part of the course

Foundations of Inference in R

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Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# From previous exercise: bootstrap t-confidence interval
one_poll_boot %>%
  summarize(
    lower = p_hat - 2 * sd(stat),
    upper = p_hat + 2 * sd(stat)
  )
  
# Manually calculate a 95% percentile interval
one_poll_boot %>%
  summarize(
    lower = ___(stat, p = ___),
    upper = ___
  )
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