## How to Find a Critical Value for a Right-Tailed Test

Main > Critical Values & Hypothesis Testing > Find a critical value

A z-table and critical values are used in hypothesis testing in statistics. Critical values help you to decide when to accept or reject a null hypothesis. Finding a critical value for a right-tailed test will have a familiar feel to it if you are used to looking up areas in a z-table (which should have been covered by this point in any elementary statistics class). Even if you aren’t familiar with using a z-table, this article walks you through the process, step-by-step, with images.

Sample question: Find a critical value in the z-table for an aplha level of 0.0079.

Step 1: Draw a diagram, like the one above. Shade in the area in the right tail.
This area represents α. A diagram helps you to visualize what area you are looking for (i.e. if you want an area to the right of the mean or the left of the mean.

Step 2: Subtract alpha (α) from 0.5.
0.5-0.0079 = 0.4921.

Step 3: Find the result from step 2 in the center part of the z-table.
The closest area to 0.4921 is 0.4922 at z=2.42.

The closest to .4921 is the value (.4922) at z = 2.42

That’s it!

## 23 thoughts on “How to Find a Critical Value for a Right-Tailed Test”

1. Angie Widdows

This was a good example. One thing I have a question about. Why is everything subtracted (or added) to 0.5. Why is that considered the magic number

2. Stephanie

The area under the curve is 1.0. Half of this is 0.5. Subtracting from 0.5 gives you the area of the critical region.

3. Lisa Barcomb

This right tailed critical value is just like the left but on the right side these problems are the ones that I like now because I know how to do them. And having an example makes all the difference in the world

4. Vanessa DuBarry

This example really helped.I love that this site exists because with mathzone I dont understand anyhthing and they dont explain.

5. Donna Allen

I agree with Vanessa. For me, sometimes the guided solution in mathzone is a bit daunting and doesn’t always explain everything step by step. Your example was very helpful.

6. Stephanie

Jennifer,
I don’t have enough information to answer your question but it sounds like you need to look something up in the t-table. That has degrees of freedom.
Stephanie

7. Donna Allen

Maybe I’m missing something very obvious, but I don’t understand how to tell if a word problem is left-tailed, right-tailed, or two-tailed.

8. Lauren Schultz

I am sortof confused on this topic. I cant figure out when to use the t-table. I have only used the z-table and have been some how getting the answers…

9. Mary Johnson

Like Jennifer I am also confused when it comes to degrees of freedom. Mathzone is not much help and as soon as I think I have it figured out, I get the next problem wrong.

10. Angella Clarke

I finally figured out how to find the closest area. That was very challenging for me, but with a lot of practice, I finally know how to do it.

11. Tammy Sutton

I’m glad I took a look at this, it’s going to be a great help with the exam.

I still get a little confused but it’s the left that confuses me more, maybe because they are negative?

12. Alison Bryant

This was really helpful, I kept coming up with the wrong answer until I realized that in needed to subtract from .5

13. marline ruddy

em..just curious..after we got those value from z table, we should make like a conclusion and interpret those value..how to interpret the result and is the null hypothesis should be rejected or not? how to interpret those actually bcause i still don’t really understand the way of interpreting those result..please

14. Andale

Kelsey,

It’s just an arbitrary figure to demonstrate how to find any critical value. The steps could apply for alpha of .57,.99, .66 etc.

Regards,
Stephanie

15. Joshua Pierce

I don’t get it, I working on a problem that says alpha = 0.08

so if I take .5-.08 I get .42 now I have no clue where this Z table is and if its Standard Normal Distribution that in my book I look it up and get .6628 now MuMathLab says Z score = 1.41 I have no clue how they are getting this number. Also it said it’s a right tailed so yeah.

16. Andale

Hi, Joshua,
Thank you for your question. Unfortunately, time constraints prevent me from answering math questions in the comments. Could you post your question on our forums? One of our mods would be glad to help.
Stephanie