Probability and Statistics > TI-83 for Statistics > how to find t critical value on ti 83

Watch the video or read the article below:

IMPORTANT: The TI-83 doesn’t have a function to calculate the t critical value directly. In other words, you won’t find it listed on a menu as something like “invT”. However, youcancalculate it; it just takes a couple of extra steps.

- if you want a t critical value for a two tailed test, follow the steps below. The
confidence interval limits are the same as the t critical values.- if you want the t critical value for a one tailed test, you can’t use the TI83 unless you program it (see this video for instructions ).

## How to Find T Critical Value on TI 83: Steps

**Sample Question:** Calculate the two-talied t-critical value for 36 degrees of freedom (df = 36) for an alpha level of 0.05 (α = 0.05).

Step 1: Press the “STAT” key, then press the left arrow key to arrive at the Tests menu.

Step 2: Press “8” for TInterval.

Step 3: Arrow right to choose STATS. Press ENTER.

Step 3: Change the values in the list. For this sample question:

- Set the mean (Xbar) to 0
- Set Sx to the square root of your sample size. The sample size is df+1, so for this example press √37.
- Set n as your sample size. For this example, it’s 37.
- Set your confidence level, which is 1 – α For this example, set it to .95.

Step 4: Highlight CALCULATE and then press Enter. The t-critical value is The same as the given confidence level limits: 2.028.

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THIS IS NOT CRITICAL VALUE

Echech,

I’ve double checked it and I don’t see an error. Can you be a little more specific about the problem you see with the critical value? Thanks.

echech is right, this isn’t how to find a critical value. following these steps gives you the confidence interval (which you need the critical value to find)

Hello, Sara,

The confidence limits are the same as the two tailed t critical value.

You do not need to know the critical value to find these limits — all you need are the alpha level and degrees of freedom.

Regards,

Stephanie

Lets look at why this method does find the t critical value.

first the formula for confidence interval (x bar – error, x bar + error) or (x-E,x+E) for simpler notation.

E=t_(alpha/2)*(s/SquareRoot(n))

so if we let s=SquareRoot(n) E will be the t critical value for a two tail test.

E=t_(alpha/2)*(SquareRoot(n)/SquareRoot(n)) so the two square roots will cancel.

Now if x = 0, our confidence interval becomes (0-E,0+E) or just (-E,E)

putting it all together we get that the confidence interval is (-t_(alpha/2),t_(alpha/2))

Hence we can get the two tailed critical value using the confidence interval.

If you want a one tail critical value you must double the alpha value and take either the negative (left tail) or positive (right tail).

Hope this helps explain why this works!