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

Main > Critical Values & Hypothesis Testing > Critical value for a left-tailed test

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). Even if you haven’t used a z-table before, this article walks you through the process.

Sample question: find the critical value in the z-table for α=.012 (left-tailed test).

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 (because you’re looking for a critical value for a left-tailed test).
This area represents alpha, α — the “alpha level.”

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 (left-tail critical values are always negative).
-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.

## 28 thoughts on “How to Find a Critical Value for a Left-Tailed Test”

1. Angie Widdows

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. Stephanie

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

3. Lisa Barcomb

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

4. Vanessa DuBarry

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.

5. Donna Allen

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.

6. Vanessa DuBarry

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

7. Stephanie

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

8. Donna Allen

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.

9. Catherine Flanagan

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.

10. Stephanie

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

11. Arturo

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

12. crystal lydick

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.

13. Cheryl

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