Non-Technical Hypothesis Testing

Introduction/Scenario

The average height of humans in the world is 162cm. This is our population.

Let’s say we recently found an unknown island and there were people living in it. There were millions of people living on the island and we wanted to calculate what their average height is. Because we can’t collect millions of heights (takes a long time), we collect a sample of the population. In the sample, the average height is 250cm.

WOW these people are tall! But how do we determine how tall they are versus the world’s population? This is where hypothesis testing comes in.

Establish Hypothesis

There are two possible hypothesis:
- the people on the island are average height (Null Hypothesis)
- the people on the island are not average height (Alternative Hypothesis)

You may be wondering…of course they are not average height, they are giants! That’s true from a logical perspective, but how do we confirm this?

The average height of the population is 162cm, but not all humans are 162cm. Some can be 140cm, 155cm, 170cm, or even 216cm! But it’s safe to say humans that are farther from the average are unlikely. How many people are as tall as Shaquille O’Neal (216cm)? Not many.

Now we need to compare our sample average with the population average. And that is exactly what hypothesis testing is: comparing our…