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The Z Critical Value is a statistical value used to determine the likelihood of a certain event occurring in a normal distribution. To find this value on a TI-84 calculator, follow these steps:
1. Press the “2nd” button, then press “VARS” to access the distribution menu.
2. Scroll down and select “invNorm(” to enter the inverse normal function.
3. Enter the desired level of significance (alpha) as a decimal, followed by a comma.
4. Then, enter 0 for the mean and 1 for the standard deviation, separated by a comma.
5. Press “Enter” to calculate the Z Critical Value, which will be displayed on the screen.
This value can be used in various statistical calculations to determine the probability of a certain outcome.
Find the Z Critical Value on a TI-84 Calculator
Whenever you conduct a hypothesis test, you will get a test statistic as a result. To determine if the results of the hypothesis test are statistically significant, you can compare the test statistic to a Z critical value. If the absolute value of the test statistic is greater than the Z critical value, then the results of the test are statistically significant.
To find the Z critical value on a TI-84 calculator, we can use the following function:
invNorm(probability, μ, σ)
where:
- probability: the significance level
- μ: population mean
- σ: population standard deviation
You can access this function on a TI-84 calculator by pressing 2nd and then pressing vars. This will take you to a DISTR screen where you can then use invNorm():
This tutorial shares several examples of how to use the invNorm() function to find Z critical values on a TI-84 calculator.
Example 1: Z Critical Value for a Left-Tailed Test
Question: Find the Z critical value for a left-tailed test with a significance level of 0.05.
Answer: invNorm(.05, 0, 1) = -1.6449
Interpretation: If the test statistic of the test is less than -1.6449, then the results of the test are statistically significant at α = 0.05.
Example 2: Z Critical Value for a Right-Tailed Test
Question: Find the Z critical value for a right-tailed test with a significance level of 0.10.
Answer: invT(1-.10, 0, 1) = 1.2816
Example 3: Z Critical Value for a Two-Tailed Test
Question: Find the Z critical value for a two-tailed test with a significance level of 0.05.
Answer: invNorm(.05/2, 0, 1) = -1.96, 1.96
Interpretation: Since this is a two-tailed test, we actually have two critical values: -1.96 and 1.96. If the test statistic of the test is less than -1.96 or greater than 1.96, then the results of the test are statistically significant at α = 0.05.