Probability and Statistics > TI 83 > Critical z value TI 83

## Critical z value TI 83

A critical value in a hypothesis test separates the region where the hypothesis will be rejected from the region where the hypothesis will not be rejected. You could use the equation above to find the z-score; with a little **arithmetic**, you can look up a critical value in a z-table, or you can use the **InvNorm** function on the **TI-83 graphing calculator**.

Find more help for the TI 83 and statistics by visiting the main TI 83 for statistics menu.

## Critical z value TI 83: Steps

InvNorm can be used in a couple of different ways. The first problem shows you how to find a critical value (a z-score) for a given alpha level for example, α=0.05. The second problem shows you how to use InvNorm find a specific score for data with a normal distribution.

**Sample Problem #1**: Find the critical z value for α=0.05.

Watch the video or read the steps below:

**Step 1:** Press 2nd VARS 3. This displays **InvNorm(** on the home screen.

**Step 2:** Type one of the following:

0.05 (for a one tailed test)

0.05/2 (for a two tailed test).

Not sure? See: One Tailed Test or Two.

**Step 3:** Press the ) button.

**Step 4: **Press Enter.

- -1.64 is the z-score for the left tail.
- 1.64 is the z-score for the right tail (because the normal distribution is symmetrical).
- -1.96 is the area in the left tail for a two tailed test
- 1.96 is the area in the right tail for a two tailed test (because the normal distribution is symmetrical).

**Sample Problem #2**: An end of semester exam is normally distributed with a mean of 85 and a standard deviation of 10. Find the score at the 90th percentile with the InvNorm function.

**Step 1:** Press 2nd VARS 3. This displays **InvNorm(** on the home screen.

**Step 2:** Type .90,85,10.

**Step 3:** Press the ) button.

Your display should read **InvNorm(.9, 85, 1, 0)**.

**Step 4:** Press ENTER. This returns **97.82**. That means that 90% of students will have scores below 97.82.

That’s it! Like the explanation?

That’s how to find a Critical z value TI 83!

**Tip**: The first entry on InvNorm should be a number between 0 and 1.

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