Hypothesis Test For Difference Of Means Calculator

Hypothesis Test Formula:

\[ Z = \frac{Mean1 - Mean2}{\sqrt{\frac{\sigma1^2}{n1} + \frac{\sigma2^2}{n2}}} \]

Mean1 (value):

Mean2 (value):

σ1 (std dev):

n1 (count):

σ2 (std dev):

n2 (count):

Z-Score:

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1. What is Hypothesis Test For Difference Of Means?

The Hypothesis Test for Difference of Means is a statistical method used to determine whether there is a significant difference between the means of two independent populations. It calculates a Z-score that helps determine if observed differences are statistically significant or due to random chance.

2. How Does the Calculator Work?

The calculator uses the Z-test formula:

\[ Z = \frac{Mean1 - Mean2}{\sqrt{\frac{\sigma1^2}{n1} + \frac{\sigma2^2}{n2}}} \]

Where:

\( Mean1 \) — Mean of the first sample
\( Mean2 \) — Mean of the second sample
\( \sigma1 \) — Standard deviation of the first sample
\( n1 \) — Sample size of the first group
\( \sigma2 \) — Standard deviation of the second sample
\( n2 \) — Sample size of the second group

Explanation: The formula calculates the standardized difference between two sample means, accounting for the variability and sample sizes of both groups.

3. Importance of Z-Score Calculation

Details: The Z-score helps determine statistical significance in hypothesis testing. A higher absolute Z-score indicates stronger evidence against the null hypothesis (that there is no difference between the means).

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test?
A: Use this test when you have two independent samples and want to test if their means are significantly different, assuming normal distribution and known population variances.

Q2: What does the Z-score value mean?
A: The Z-score represents how many standard errors the difference between means is from zero. Typically, |Z| > 1.96 indicates statistical significance at α = 0.05 level.

Q3: What are the assumptions of this test?
A: The test assumes that both samples are normally distributed, independent of each other, and that population variances are known or sample sizes are large (n ≥ 30).

Q4: When should I use t-test instead of z-test?
A: Use t-test when population variances are unknown and sample sizes are small (n < 30), or when working with dependent samples (paired t-test).

Q5: How do I interpret negative Z-scores?
A: A negative Z-score indicates that Mean1 is less than Mean2. The absolute value determines the significance level regardless of the sign.