Critical Values > Z Alpha/2 (za/2)

## What is Z Alpha/2?

If you have a question asking you to find z alpha/2, you’re being asked to find an alpha level’s z-score for a two tailed test.

Alpha levels are related to confidence levels: to find **alpha**, just subtract the confidence interval from 100%. for example, the alpha level for a 90% confidence level is 100% – 90% – 10%.

To find **alpha/2**, divide the alpha level by 2. For example, if you have a 10% alpha level then alpha/2 is 5%.

## How to find z α/2

You have three main options:

- Use known values for z alpha/2.
- Use a z-table.
- Use the TI-83/84.

## 1. (Easiest Way) Use known values for z alpha/2.

You don’t actually have to look up z alpha/2 in a z-table every time. For most statistical tests, you’ll probably be using one of four confidence intervals (90%, 95%, 98% and 99%). The z alpha/2 for each confidence level is always the same:

## 2. Use a Z-Table

Step 1: **Find the alpha level.** *If you are given the alpha level in the question (for example, an alpha level of 10%), skip to step 2.* Subtract your confidence level from 100%. For example, if you have a 95 percent confidence level, then 100% – 95% = 5%.

Step 2: Divide the amount you found in Step 1 by 2 to get the alpha level for a two-tailed test:

.50/2 = 2.5 percent.

Step 3: Subtract Step 2 from 50%:

50% – 2.5% = 47.5%

Step 4: Convert Step 3 to a decimal and find that area in the center of the z-table.

The closest z-score to 47.5 percent (.475) is at z=1.96.

**Note**: This step depends on using the right-hand z-table on this site. There *are* **several different possible z-table layouts**, so you may get a different answer if you use a different z-table. I would suggest using the same z-table when learning how to look up areas/z-scores until you get the hang of it…then you should be able to use any z-table you come across.

### TI-83 / TI-84

Step 1: Press “2nd” and then press “VARS”.

Step 2: Select “invNorm” and then press “ENTER.”

Step 3: Type in the percentage for alpha/2 from the above table. For example, type in 0.005 for a 99% confidence level.

Step 4: Type a closing parentheses “)” and then press ENTER.

The result will be the z-score for the left tail (in this example, -2.576). As the normal distribution curve is symmetrical, the cutoff for the right tail is the opposite: 2.576.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.

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In the one to solve it for the calculator how are you getting .005 for 99%?

It should be .05. Now fixed. Thanks!

On the calculator I think it should be .005 for 99% and .05 for 90% because you’re entering decimal value not percentage.

.005=99% = .5%=99%

.05=90% = 5%=90%

The confusion may have come with the table being in percentages and the explanation being in decimal.

You’re right. I missed a zero when I wrote 0.05. Thanks for spotting that :)

If the confidence interval was given 96% then how we find the infinity?

Hareem,

Can you clarify what you mean by “find the infinity?”

Thanks.

How can I get the alpha of 0.5 prbability and df of 3?

What table or distribution are you using?