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Left Tailed Test or Right Tailed Test ? How to Decide in Easy Steps

Probability and Statistics > Critical Values & Hypothesis Testing > Left Tailed Test or Right Tailed Test ?

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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.

Left Tailed Test or Right Tailed Test. How to Decide in Hypothesis Testing.

Area under a normal distribution curve. Two tails (both left and right) are shaded.

Basic Hypothesis Testing Steps

  1. 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!).
  2. 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.

right of z score2

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.

That’s it!

Note: This next picture represent the phrase “less than 25%”. You can see that it would be a left-tailed test from the picture, as the tail is shaded on the left.
Normal Distribution curve with a shaded tail

Left Tailed Test or Right Tailed Test ? How to Decide in Easy Steps was last modified: September 4th, 2015 by Stephanie

8 thoughts on “Left Tailed Test or Right Tailed Test ? How to Decide in Easy Steps

  1. Donna Allen

    Thank you for posting this. It seems simpler, now. Once I saw the graph it helped me visualize what the word problem is saying.

  2. Jennifer Thomas

    Thank you. I went through this chapter not understanding how to determine this. I didn’t realize how easy it really was. Now if I can only grasp when to reject and when to accept a claim! :0)

  3. Vanessa DuBarry

    Yes by looking at this example it makes more sense and it does make it a little bit easier. And by this I learned the importance of drawing this graphs to get the answer.

  4. Rebecca Gamble

    Even after completing the final I still do not understand hypotheses. Its like greek! And i hate not understanding this, because according to some this was the easiest section in Statistics.

  5. Mike

    Thanks this really helped me understand something very important which my college lecturers notes didn’t explain

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