Z-Test Calculator

Find the one-sample z-statistic.

z-statistic 2

Formula: z = (x̄ − μ) ÷ (σ ÷ √n)

Step-by-step with your numbers:

1. Values used:

2. Sample mean = 105

3. Population mean = 100

4. Population SD = 15

5. Sample size = 36

7. z-statistic = 2

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The z-test compares a sample mean to a population mean when the population SD is known.

The math behind it

z = (sample mean − population mean) ÷ (population SD ÷ √n).

x̄ 105, μ 100, σ 15, n 36 → z 2.0.

z vs t?

Use z when the population SD is known and n is large; otherwise use t.