# Z Test Calculator Run one-sample Z tests for a mean with known population standard deviation or a single population proportion > Canonical page: https://elysiatools.com/en/tools/z-test-calculator - **Category:** Math & Numbers - **Keywords:** z test, normal test, mean test, proportion test, p value, calculator ## Overview The Z Test Calculator is a statistical utility designed to perform one-sample Z tests for either a population mean or a population proportion. By inputting your sample statistics and known population parameters, the tool instantly calculates the Z-statistic, P-value, and determines whether to reject the null hypothesis based on your chosen significance level (alpha). It is ideal for researchers, analysts, and quality control professionals who need to evaluate sample data against established population metrics. ## Inputs - **Test Type** (select) - **Sample Mean** (number) - **Hypothesized Mean** (number) - **Population Standard Deviation** (number) - **Sample Size** (number) - **Success Count** (number) - **Trial Count** (number) - **Hypothesized Proportion** (number) - **Alternative Hypothesis** (select) - **Alpha** (number) - **Decimal Places** (number) ## When to use - When you need to compare a sample mean to a known population mean and the population standard deviation is already known. - When evaluating whether a sample proportion significantly differs from a hypothesized population proportion. - When conducting hypothesis testing with large sample sizes where the normal distribution can be assumed. ## How it works - Select the test type: choose 'Mean' for continuous data or 'Proportion' for categorical success/failure data. - Enter your sample statistics, such as the sample mean and size, along with the hypothesized population parameters. - Set your alternative hypothesis (two-sided, greater, or less) and the desired alpha level (e.g., 0.05). - The calculator computes the Z-statistic and P-value, outputting a clear JSON result indicating whether to reject the null hypothesis. ## Use cases - Quality control managers testing if a new manufacturing batch's average weight differs from the historical population mean. - Marketers determining if the conversion rate of a new landing page is significantly higher than the industry standard proportion. - Researchers verifying if survey results from a specific demographic deviate from known national census proportions. ## Frequently asked questions ### What is the difference between a Z-test and a T-test? A Z-test is used when the population standard deviation is known or the sample size is very large. A T-test is used when the population standard deviation is unknown and must be estimated from the sample. ### What does the alpha value represent? Alpha is the significance level, representing the probability of rejecting the null hypothesis when it is actually true. A common default is 0.05 (5%). ### Can I perform a one-sided Z-test? Yes, you can select 'Greater Than' or 'Less Than' in the Alternative Hypothesis dropdown to run a one-sided test. ### What inputs are required for a proportion Z-test? You need the success count, total trial count, and the hypothesized population proportion. ### What does 'rejectNull: true' mean in the output? It means the calculated P-value is less than your specified alpha level, indicating statistically significant evidence against the null hypothesis. ## Related tools - [Average Calculator](https://elysiatools.com/en/tools/average-calculator): Compare arithmetic, geometric, and harmonic averages for a numeric dataset in one place - [Confidence Interval Calculator](https://elysiatools.com/en/tools/confidence-interval-calculator): Calculate confidence intervals for a sample mean or proportion using either raw data or summary statistics - [Heat Exchanger LMTD Calculator (Log Mean Temperature Difference)](https://elysiatools.com/en/tools/heat-exchanger-lmtd): Compute the Log Mean Temperature Difference (LMTD) of a heat exchanger for parallel or counter flow. Parallel flow: ΔT₁ = T_h,in - T_c,in and ΔT₂ = T_h,out - T_c,out; counter flow: ΔT₁ = T_h,in - T_c,out and ΔT₂ = T_h,out - T_c,in. LMTD = (ΔT₁ - ΔT₂)/ln(ΔT₁/ΔT₂), or ΔT₁ when ΔT₁ = ΔT₂. 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