2 Sample Z Test Calculator Statistics

2 Sample Z Test Formula:

\[ Z = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \]

Mean1 (x̄₁):

Mean2 (x̄₂):

SD1 (σ₁):

SD2 (σ₂):

Sample Size1 (n₁):

Sample Size2 (n₂):

Z-Score:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the 2 Sample Z Test?

The 2 Sample Z Test is a statistical method used to determine whether there is a significant difference between the means of two independent groups when the population standard deviations are known. It's commonly used in hypothesis testing to compare two sample means.

2. How Does the Calculator Work?

The calculator uses the 2 Sample Z Test formula:

\[ Z = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}}} \]

Where:

\( \bar{x}_1 \) — Mean of sample 1
\( \bar{x}_2 \) — Mean of sample 2
\( \sigma_1 \) — Standard deviation of population 1
\( \sigma_2 \) — Standard deviation of population 2
\( n_1 \) — Size of sample 1
\( n_2 \) — Size of sample 2

Explanation: The formula calculates the standardized difference between two sample means, accounting for the variability and size of each sample.

3. Importance of Z-Test Calculation

Details: The Z-test is crucial for determining if observed differences between two groups are statistically significant or due to random chance. It's widely used in research, quality control, and various scientific fields.

4. Using the Calculator

Tips: Enter the means, population standard deviations, and sample sizes for both groups. All values must be valid (standard deviations > 0, sample sizes ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: When should I use a 2 Sample Z Test?
A: Use it when you have two independent samples, known population standard deviations, and want to test if their means are significantly different.

Q2: What's the difference between Z-test and t-test?
A: Z-test uses known population standard deviations, while t-test uses sample standard deviations and is more appropriate for smaller sample sizes.

Q3: How do I interpret the Z-score?
A: A larger absolute Z-score indicates a greater difference between means. Typically, |Z| > 1.96 suggests statistical significance at α = 0.05.

Q4: What are the assumptions of the 2 Sample Z Test?
A: The test assumes independent samples, normally distributed populations, and known population standard deviations.

Q5: Can I use this test for proportions?
A: For comparing proportions, you would use a different version of the Z-test specifically designed for proportion data.