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You can use the invNorm() function on a TI-84 calculator to find z critical values associated with the .
This function uses the following syntax:
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():
The following examples show how to use this function in practice.
Example 1: Z-Critical Value for One-Tailed Tests
Suppose a researcher is conducting a left-tailed hypothesis test using α = .05. What is the z-critical value that corresponds to this alpha level?
The answer is z = -1.64485.
Suppose a researcher is conducting a right-tailed hypothesis test using α = .05. What is the z-critical value that corresponds to this alpha level?
The answer is z = 1.64485.
Example 2: Z-Critical Value for Two-Tailed Tests
To find this critical value, we can use the formula 1 – α/2. In this case, we will use 1 – .05/2 = .975 for the probability:
The answer is z = 1.96.
Example 3: Z-Critical Value for Cut-Off Scores
Suppose the scores on a particular exam are normally distributed with a mean of 70 and a standard deviation of 8. What score separates the top 10% from the rest?
The answer is 80.25.
Suppose the heights of males in a particular city are normally distributed with a mean of 68 inches and a standard deviation of 4 inches. What height separates the bottom 25% from the rest?
The answer is 65.3 inches.