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

Critical Values and Z-Tables, Hypothesis Testing 23 Comments

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). This article shows you how to find α=.079 for a right-tailed test.

right of z score2

Step 1: Draw a diagram, like the one above. Shade in the area in the right tail.
This area represents α.
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.

That’s it!

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23 Responses to “How to Find a Critical Value for a Right-Tailed Test”

  1. Angie Widdows said:

    Oct 15, 09 at 9:36 am

    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 said:

    Oct 17, 09 at 5:23 am

    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 said:

    Oct 18, 09 at 10:22 am

    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. Stephanie said:

    Oct 19, 09 at 12:39 pm

    Great! I’m glad this is helping.

  5. Jennifer Thomas said:

    Oct 25, 09 at 8:14 pm

    This is helpful. Any time I need a refresher (like before the exam) I always refer back to this site.

  6. Vanessa DuBarry said:

    Oct 27, 09 at 10:55 am

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

  7. Donna Allen said:

    Oct 27, 09 at 2:08 pm

    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.

  8. Jennifer Thomas said:

    Oct 27, 09 at 5:31 pm

    How do we find a critical value if given the degrees of freedom? I’m confused and Mathzone hasn’t helped me.

  9. Stephanie said:

    Oct 28, 09 at 6:49 am

    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

  10. Rebecca Gamble said:

    Oct 31, 09 at 9:46 pm

    I’m confused. .5-.079=.421 how did the you get .4921?

  11. Donna Allen said:

    Nov 02, 09 at 2:57 pm

    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.

  12. Lauren Schultz said:

    Nov 12, 09 at 11:40 am

    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…

  13. Lisa Barcomb said:

    Nov 12, 09 at 7:18 pm

    Well doing these kinds of problems are okay. I guess its because I know how to do them. And when you know how to do something you don’t mind learning.

  14. Mary Johnson said:

    Nov 17, 09 at 8:46 am

    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.

  15. Angella Clarke said:

    Nov 20, 09 at 2:12 pm

    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.

  16. Tammy Sutton said:

    Dec 07, 09 at 3:30 pm

    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?

  17. Alison Bryant said:

    Mar 29, 10 at 5:53 pm

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

  18. Tauata Loto'aniu said:

    Apr 24, 12 at 3:04 pm

    thank you. This solution is really help and thanks again for showing the step of how to find the critical value

  19. marline ruddy said:

    Dec 29, 12 at 5:06 pm

    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

  20. kelsey said:

    Feb 13, 13 at 7:52 pm

    i dont get where the 0.079 come from?

  21. Andale said:

    Feb 18, 13 at 7:49 am

    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

  22. Joshua Pierce said:

    Apr 20, 13 at 2:14 pm

    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.

  23. Andale said:

    Apr 23, 13 at 12:50 pm

    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