When the null is true

In this exercise, you will run an experiment: what happens when you conduct a hypothesis test when you know that the null hypothesis is true? You hope that you will retain the null hypothesis, but there's always a chance that you will make a statistical error.

To begin the experiment, we have created a new explanatory variable called coinflip that captures the result of a fair coin toss for every subject. With that variable in hand you can pose the following null hypothesis:

$$ H_{0}: p_{heads} - p_{tails} = 0 $$

This claims that there is no difference in the proportions that favor the death penalty between the people that flipped "heads" and those that flipped "tails". Since coinflip was formed independently of cappun, we know that this null hypothesis is true. The question is: will your test reject or retain this null hypothesis?

This exercise is part of the course

Inference for Categorical Data in R

View Course

Hands-on interactive exercise

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

# Inspect coinflip
gssmod %>%
  select(coinflip)

# Compute two proportions
___ <- gssmod %>%
  group_by(coinflip) %>%
  summarize(prop_favor = mean(___ == ___)) %>%
  pull()
  
# See the result
p_hats

Edit and Run Code