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Hypothesis Testing Basics: One Tail or Two?
In a hypothesis test, you have to decide if a claim is true or not. Before you can figure out if you have a left tailed test or right tailed test, you have to make sure you have a single tail to begin with. A tail in hypothesis testing refers to the tail at either end of a distribution curve.
Basic Hypothesis Testing Steps
- Decide if you have a one-tailed test or a two-tailed test (How to decide if a hypothesis test is a one-tailed test or a two-tailed test). If you have a two-tailed test, you don’t need to worry about whether it’s a left tailed or right tailed test (because it’s both!).
- Find out if it’s a left tailed test or right tailed test (see below).
If you can sketch a graph, you can figure out which tail is in your test.
Left Tailed Test or Right Tailed Test ?
Sample question: You are testing the hypothesis that the drop out rate is more than 75% (>75%). Is this a left-tailed test or a right-tailed test?
Step 1: Write your null hypothesis statement and your alternate hypothesis statement. This step is key to drawing the right graph, so if you aren’t sure about writing a hypothesis statement, see: How to State the Null Hypothesis.
Step 2: Draw a normal distribution curve.
Step 3: Shade in the related area under the normal distribution curve. The area under a curve represents 100%, so shade the area accordingly. The number line goes from left to right, so the first 25% is on the left and the 75% mark would be at the left tail.
The yellow area in this picture illustrates the area greater than 75%. From this diagram you can clearly see that it is a right-tailed test, because the shaded area is on the right.