Test Statistic Calculator

Test Statistic Formula:

\[ z = \frac{x - \mu}{\sigma / \sqrt{n}} \]

Sample Mean (x):

Hypothesized Mean (μ):

Standard Deviation (σ):

Sample Size (n):

Test Statistic (z):

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1. What Is The Test Statistic?

The test statistic (z-score) measures how many standard errors a sample mean is from the hypothesized population mean. It's used in hypothesis testing to determine statistical significance.

2. How Does The Calculator Work?

The calculator uses the formula:

\[ z = \frac{x - \mu}{\sigma / \sqrt{n}} \]

Where:

\( x \) — Sample mean
\( \mu \) — Hypothesized population mean
\( \sigma \) — Population standard deviation
\( n \) — Sample size

Explanation: The formula calculates how many standard errors the sample mean is away from the hypothesized mean, which helps determine if the difference is statistically significant.

3. Importance Of Test Statistic Calculation

Details: Calculating the test statistic is crucial for hypothesis testing in statistics. It helps researchers determine whether to reject the null hypothesis and is fundamental in making data-driven decisions across various fields including science, medicine, and social sciences.

4. Using The Calculator

Tips: Enter the sample mean, hypothesized population mean, population standard deviation, and sample size. All values must be valid (standard deviation > 0, sample size ≥ 1).

5. Frequently Asked Questions (FAQ)

Q1: When should I use this test statistic?
A: This z-test statistic is appropriate when you know the population standard deviation and have a sufficiently large sample size (typically n ≥ 30).

Q2: What does the z-value represent?
A: The z-value represents how many standard errors your sample mean is from the hypothesized mean. Higher absolute values indicate greater statistical significance.

Q3: What's the difference between z-test and t-test?
A: Use z-test when population standard deviation is known; use t-test when it's unknown and must be estimated from the sample.

Q4: How do I interpret the z-score?
A: Typically, a z-score beyond ±1.96 indicates statistical significance at the 0.05 level, and beyond ±2.58 at the 0.01 level.

Q5: What if my population standard deviation is unknown?
A: If population standard deviation is unknown, you should use a t-test instead, which uses sample standard deviation.