• Recognize Type I and Type II errors and their consequences.

Type I error

A Type I error occurs when a true null hypothesis is rejected.

Let’s explore the sampling distribution of sample proportions under the null hypothesis.

The figure illustrates our hypothesis test decision rule. If the actual sample proportion is greater than [latex]0.275[/latex] or less than [latex]0.205[/latex], we would reject the null hypothesis and conclude that there was a change in vaping rates.

But, what if the vaping rates did NOT change and you happened to select a sample proportion in the tails portion (shaded light blue) of the distribution? In other words, you selected a “lucky” sample that was simply unusual given that the null hypothesis of no change was true ([latex]0.24[/latex]), which resulted in a small enough P-value to reject the null hypothesis. In this case, you would have committed a type I error.