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

Critical Values and Z-Tables, Hypothesis Testing 28 Comments

Finding a critical value for a left-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=.012 for a left-tailed test. If you like our easy to follow explanations of statistics, check out our easy to follow book, which has hundreds more examples, just like this one.

Area under a normal distribution curve (one tail)

Area under a normal distribution curve (alpha is shaded yellow)

Step 1: Draw a diagram, like the one above. Shade in the area in the left tail.
This area represents α.
Step 2:Subtract alpha (α) from 0.5.
0.5-0.012=0.488.
Step 3: Find the result from step 2 in the center part of the z-table.
The closest area to 0.488 is at z=2.26. If you can’t find the exact area, just find the closest number and read the z value for that number.
Step 4:Add a negative sign to Step 3.
-2.26.
That’s it! Like the explanation? Check out our statistics how-to book, with a how-to for every elementary statistics problem type.

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28 Responses to “How to Find a Critical Value for a Left-Tailed Test”

  1. Angie Widdows said:

    Oct 15, 09 at 9:40 am

    This was also a helpful example. One problem that I seem to have with these types of problems is figuring out what value on the table is closest to the number we are to look for. I tend to get in a hurry and pick the wrong number. That is something I have been trying to work on.

  2. Jennifer Thomas said:

    Oct 17, 09 at 7:21 am

    So if it’s in between, we could use 3.03 or 3.04 and both would be considered correct?

  3. Stephanie said:

    Oct 17, 09 at 8:45 am

    Both would be considered correct in my book. Usually Mathzone will pick problems that aren’t ambiguous like that but if you are marked wrong because of that type of error–let me know and I’ll fix it.
    Stephanie

  4. How to Do Everything Statistics » How to Support or Reject a Null Hypothesis said:

    Oct 17, 09 at 10:01 am

    [...] critical value. You should have already covered that topic by this point, but here is a how-to on finding the critical value for a left-tailed test as a reminder. You may need to find a right-tailed or two-tailed [...]

  5. Lisa Barcomb said:

    Oct 18, 09 at 10:17 am

    yeah at first I was reading this and did not really understand it but then all of a sudden it came to me and then once I saw the bell and figured out the critical area then it was really simple. I noticed that we had some of these problems on our homework and they started to become easy

  6. Vanessa DuBarry said:

    Oct 27, 09 at 11:00 am

    This also helped me because I didnt know we had to put a negative sign fot the problems with left tailed which I should of caught because its the left side and its always negative, so it helps to have examples like these to help with those mistakes.

  7. Donna Allen said:

    Oct 27, 09 at 2:13 pm

    I have had a few instances where mathzone has marked my question incorrect because of variation in the number that could be used from the z-table. This is good to know for future reference.

  8. Vanessa DuBarry said:

    Oct 29, 09 at 11:19 am

    I dont know why I dont understand getting the critical value. in this example it says to subtract 0.5-0.012 but here you said the answer is 0.4988 but when I subtract it gives me 0.488 so I dont know what IM I doing wrong?.. like for example I have a=0.05 so I subtract that from 0.5 and it gives me 0.45 but that its wrong because the answer is 0.4505 how? please help what Im I doing wrong

  9. Stephanie said:

    Oct 29, 09 at 1:29 pm

    You just caught a type. 0.5-0.012 is indeed 0.488.

    You are looking for the closest value in the z-table. It doesn’t have every number. So if you are looking for .45, the closest value may be .4505. That isn’t an “exact” answer, but it will work for your calculations. The TI-83 will give you a more exact answer, but even that isn’t perfect :)

    Stephanie

  10. Donna Allen said:

    Nov 02, 09 at 3:03 pm

    I understand how to arrive at the answer. I’m just not sure how to tell if a word problem is right-tailed or left-tailed or two-tailed.

  11. Vanessa said:

    Nov 03, 09 at 6:08 pm

    How do I determine if it the test is two tailed left tailed or right tailed?

  12. Stephanie said:

    Nov 05, 09 at 4:55 am

    Vanessa,
    This should help!

  13. How to Do Everything Statistics » How to Support or Reject a Null Hypothesis (Using a P-Value) said:

    Nov 05, 09 at 9:26 am

    [...] critical value. You should have already covered that topic by this point, but here is a how-to on finding the critical value for a left-tailed test as a reminder. You may need to find a right-tailed or two-tailed [...]

  14. Catherine Flanagan said:

    Nov 08, 09 at 8:11 am

    This website is a life-saver! I spent about ten minutes trying to understand these kinds of problems. This website explains it so easily! Thank you.

  15. cherr said:

    Nov 12, 09 at 9:49 am

    why do you have to substract it from 0.5?

  16. Stephanie said:

    Nov 12, 09 at 11:24 am

    The are under the curve is 1. So the area in the left-hand side of the curve is 0.5. You’re looking for the area 0.5-alpha.
    Stephanie

  17. Arturo said:

    Nov 22, 09 at 9:10 am

    Hi, this site seems to be very helpful to me too. I had the same problem as Vanessa dubary, I was confuse, but I think I got it all now. In my book, I have astatement to find a left tailed test with 95% confidence. that is, alpha = 1-.95=0.05. Right?? but now I just look for 0.05 in the midle of the table, I dont have to substract again 0.5-0.05 in this case. am I right??. then the answer would be -1.64

  18. Arturo said:

    Nov 22, 09 at 9:10 am

    Can we make interpolations in the Z table to find a number that is not in the table?

  19. Stephanie said:

    Nov 24, 09 at 2:41 pm

    Arturo,
    You do have to subtract. 0.5-0.05, before you look it up in the table…
    Stephanie

  20. Stephanie said:

    Dec 01, 09 at 2:40 am

    Absolutely.

  21. Statistics How To» Blog Archive » How to Support or Reject a Null Hypothesis (for a Proportion) said:

    Jan 13, 10 at 12:08 pm

    [...] 2: Find the critical value. Here is a how-to on finding the critical value for a left-tailed test as a reminder. You may need to find a right-tailed or two-tailed [...]

  22. crystal lydick said:

    Mar 27, 10 at 11:41 am

    This page really helped explain how to find a critical value for a Left-tailed test. I couldn’t figure out how to do these problems until I found this on the statistics how to forum. If it wasn’t for this forum, I would be completely lost. At least with this forum and the practically cheating book we have something to help guide us in the right direction.

  23. Cheryl said:

    Oct 25, 10 at 11:31 am

    How do I find the critical value for α=.025 for a left-tailed test? Is there a zscore table on this site?

  24. Sam said:

    Apr 14, 12 at 10:27 am

    YOU SAVED MY LIFE!!

  25. Andale said:

    Apr 14, 12 at 5:31 pm

    :)

  26. Meena said:

    May 22, 12 at 2:55 am

    That was a very simple and easy to understand example. Thank you :)

  27. Wanda said:

    Jul 22, 12 at 8:55 am

    -2.26 takes me to .0119 in the z table ??? what am I doing wrong?

  28. Andale said:

    Jul 22, 12 at 9:47 am

    Are you using this z-table?

    Stephanie