One-Sample Z-Test

Compare a sample mean to a known population mean with a known standard deviation.

Test Parameters

Sample Mean (x̄)

Population Mean (μ₀)

Pop. Std. Dev (σ)

Sample Size (n)

Test Analysis

Z-Statistic1.8257

Significance ResultNot Significantat α=0.05 level

P-Value (Two-Tailed)0.054318

Standard Error2.7386

Overview

A Z-test is a statistical test used to determine whether two population means are different when the variances are known and the sample size is large. It calculates a Z-statistic, which represents the number of standard errors the sample mean is away from the population mean under the null hypothesis.

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Pro Tips

Only use a Z-test if you know the true population standard deviation. If you only have the sample standard deviation, use a T-test instead.
Ensure your sample size is sufficiently large (n > 30) or that the population is normally distributed.
The null hypothesis (H₀) typically assumes there is no significant difference between the means.

Fun Facts

"The Z-test is based on the Normal Distribution (Z-distribution), while the T-test is based on the Student's T-distribution."
"As the sample size increases (typically n > 30), the T-distribution converges to the Normal distribution, making the Z-test and T-test results nearly identical."
"A Z-score of +1.96 or -1.96 corresponds to the boundaries of the 95% confidence interval."

Formula: z = (x̄ - μ₀) / (σ / √n)

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