Insights into Hypothesis Testing (Part 12)

Understanding Mathematics behind Type I Error and Type II Error

Let’s consider the following population.

Population 1 = {1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5}

Mean = 3, Mode = 3, Median = 3

Population 2= {3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 7, 8}

Mean = 5, Mode = 5, Median = 5

As shown in the blog of previous day if sample mean is more than 4.27 we conclude that the sample doesn’t belong to Population 1 and we commit type I error. But if the sample mean is less than 4.27 we accept the null hypothesis. Either we accept a true null hypothesis or accept a false null hypothesis. Type I error and Type II error with respect to Population I and Population mentioned above are explained by the following diagram

Type I Error and Type II Error