MathKing - Free Statistical Calculators

数学王

Inferential Statistic Calculator

Inferential

Select Test:

Test Parameters

Tail:

Significance level (α):

Effect Size:

Group name:

Sample mean (x̄):

Expected population mean (μ₀):

Sample size (n):

Population SD (σ):

When entering raw data, the tool will run the Shapiro-Wilk normality test and count outliers, as part of the test calculation.

Difference between

Z-Test One-Sample

Z-Test Two-Sample

Formula

Z = (x̄ - μ) / (σ / √n)

where:

x̄: Mean of the sample

μ: Mean of the population

σ: Standard deviation of the population

n: Sample size

Example:

If you want to know whether the average height of students in Mekarmukti (x̄) is different from the known national average height (μ), then this formula is used.

The one sample Z-Test is used to test hypotheses about the population mean.

Formula

Z = (x̄₁ - x̄₂) / √(σ₁²/n₁ + σ₂²/n₂)

where:

x̄₁: Mean of the sample 1

x̄₂: Mean of the sample 2

σ₁²: Variance of population 1

σ₂²: Variance of population 2

n₁: Sample size of sample 1

n₂: Sample size of sample 2

Example:

If you want to know whether the average test results of students in Mekarmukti (x̄₁) are different from the average test results of students in other populations (x̄₂), then this formula is used.

The two sample Z-Test is used to compare the means of two populations.