Bootstrap t-confidence interval
The previous exercises told you two things:
- You can measure the variability associated with \(\hat{p}\) by resampling from the original sample.
- Once you know the variability of \(\hat{p}\), you can use it as a way to measure how far away the true proportion is.
Note that the rate of closeness (here 95%) refers to how often a sample is chosen so that it is close to the population parameter. You won't ever know if a particular dataset is close to the parameter or far from it, but you do know that over your lifetime, 95% of the samples you collect should give you estimates that are within \(2SE\) of the true population parameter.
The votes from a single poll, one_poll
, and the data from 1000 bootstrap resamples, one_poll_boot
are available in your workspace. These are based on Experiment 2 from earlier in the chapter.
As in the previous exercise, when discussing the variability of a statistic, the number is referred to as the standard error.
This exercise is part of the course
Foundations of Inference in R
Exercise instructions
- Calculate \(\hat{p}\) and assign the result to
p_hat
. In the call tosummarize()
, calculatestat
as the mean ofvote
equalling"yes"
. - Find an interval of values that are plausible for the true parameter by calculating \(\hat{p} \pm 2SE\).
- The
lower
bound of the confidence interval isp_hat
minus twice the standard error ofstat
. Usesd()
to calculate the standard error. - The
upper
bound isp_hat
plus twice the standard error ofstat
.
- The
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# From previous exercises
one_poll <- all_polls %>%
filter(poll == 1) %>%
select(vote)
one_poll_boot <- one_poll %>%
specify(response = vote, success = "yes") %>%
generate(reps = 1000, type = "bootstrap") %>%
calculate(stat = "prop")
p_hat <- one_poll %>%
# Calculate proportion of yes votes
summarize(stat = ___) %>%
pull()
# Create an interval of plausible values
one_poll_boot %>%
summarize(
# Lower bound is p_hat minus 2 std errs
lower = ___,
# Upper bound is p_hat plus 2 std errs
upper = ___
)