Hypothesis tests

We'll be utilizing a situation very similar to what we used in Confidence intervals. This is purposeful- I want you to understand how the same situation can be applied to a confidence interval or a hypothesis test!

Imagine you're a freshman at Crammer Nation University, and that Greek Life rush has just begun. You just called it quits on your high school relationship, so you’re looking to hop right into the college action. So, you download Tinder.

You hear through the grapevine that the brothers of Sigma Apple Pi are pushing some absolute numbers on Tinder… claiming to get an average of 25 matches per day. Before you completely ignore every other fraternity and solely rush Sigma Apple Pi for their Tinder clout, you want to gather some data to determine if this claim holds its weight.

You decide to ask 30 random Sigma Apple Pi brothers for their average Tinder matches per day. Keep in mind: you’re not checking to see if every brother has exactly 25 average Tinder matches per day… there’s obviously going to be some wiggle-room. However, if the brothers’ average Tinder matches are consistently below 25… there’s a chance Sigma Apple Pi doesn’t have as much Tinder game as they claim.

In this situation, you’ve essentially set up a hypothesis test!

Hypothesis testing is a way to test a claim about a given population. It enables you to determine whether or not an outcome of a given sample was due to random chance or was statistically significant.

What’s the population in this situation? The brothers of Sigma Apple Pi.

What’s the sample? The 30 brothers that you sampled.

What’s the claim that you’re testing? That the brothers of Sigma Apple Pi actually get on average 25 Tinder matches per day.

The outcome of every hypothesis test

Without digging into the math yet, there's two potential conclusions our hypothesis test will come to based on our sample.

  • We do have enough evidence to reject Sigma Apple Pi's claim of 25 average Tinder matches per day.
  • We don't have enough evidence to reject (a.k.a. "fail to reject") Sigma Apple Pi's claim of 25 average Tinder matches per day.

To arrive to either of the above two solutions, there's 4 crucial steps that we'll take:

  1. State the hypotheses
  2. Calculate the test statistic
  3. Find the p-value
  4. Make your concluding statement

Let's dig into the key elements of each step!

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