CI via approximation
The approximation shortcut offers an alternative method of describing the sampling distribution. In this exercise, you will apply the approximation shortcut to build a confidence interval for the proportion of respondents that live in the pacific region.
When building any confidence interval, note that you use three ingredients: the point estimate (here, p_hat), the SE, and the number of standard errors to add and subtract. For a sampling distribution that is bell-shaped, adding and subtracting two SEs corresponds to a confidence level of 95%. When you use the bootstrap, you can check that the distribution is bell-shaped because you have a have the bootstrap distribution to plot. When you use the approximation, you're flying blind — well, not quite blind, but you are dependent on the "rule of thumb" to ensure that you're working with a bell shape.
This exercise is part of the course
Inference for Categorical Data in R
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
# Calculate n as the number of rows
n <- nrow(gss2016)
# Calculate p_hat as the proportion in pacific meta region
p_hat <- gss2016 %>%
___(prop_pacific = ___(___ == "___")) %>%
pull()
# See the result
p_hat