Sample size effects on bootstrap CIs

In a previous multiple choice exercise, you realized that if you resampled the data with the wrong size (e.g. 300 or 3 instead of 30), the standard error (SE) of the sample proportions was off. With 300 resampled observations, the SE was too small. With 3 resampled observations, the SE was too large.

Here, you will use the incorrect standard error (based on the incorrect sample size) to create a confidence interval. The idea is that when the standard error is off, the interval is not particularly useful, nor is it correct.

This exercise is part of the course

Foundations of Inference in R

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Exercise instructions

A function for calculating the bootstrapped t-confidence interval, calc_t_conf_int(), is shown is the script. Read the code and try to understand it.
Call calc_t_conf_int() on one_poll_boot to calculate the correct t-confidence interval.
Do the same on one_poll_boot_300, to find an incorrect interval for the resamples of size 300.
Do the same on one_poll_boot_3, to find an incorrect interval for the resamples of size 3.

Hands-on interactive exercise

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

calc_t_conf_int <- function(resampled_dataset) {
  resampled_dataset %>%
    summarize(
      lower = p_hat - 2 * sd(stat),
      upper = p_hat + 2 * sd(stat)
    )
}

# Find the bootstrap t-confidence interval for 30 resamples
calc_t_conf_int(___)

# ... and for 300 resamples
___

# ... and for 3 resamples
___

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