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?

Inspect the new coinflip variable.
Compute the proportions that FAVOR among both heads and tails values of coinflip using the dataset gssmod. Save this statistic to p_hats.

Exercise

When the null is true

Instructions 1/4