One Sample Z-Test Calculator: Hypothesis Testing Tool
Perform a one-sample z-test to determine if there is a statistically significant difference between a sample mean and a known population mean. Calculate test statistic and p-value. Free and easy-to-use online calculator.
Input Parameters
Enter your sample observations separated by commas.
The known mean of the population.
The known standard deviation of the population.
The mean value you are testing against.
Commonly used alpha levels are 0.01, 0.05, and 0.10.
Results
Test Statistic (Z):
P-value:
Conclusion:Statistically significant at α = . Reject the null hypothesis.Not statistically significant at α = . Fail to reject the null hypothesis.
Visualization
Understanding the One-Sample Z-Test
The One-Sample Z-Test is a statistical hypothesis test used to determine whether an unknown population mean is different from a specific value. It is particularly useful when you have a single sample and you know the population standard deviation.
Key Concepts:
- Null Hypothesis (H0): States that there is no significant difference between the sample mean and the population mean. Mathematically represented as: \( H_0: \mu = \mu_0 \)
- Alternative Hypothesis (H1): States that there is a significant difference. Can be two-tailed (\( H_1: \mu \neq \mu_0 \)), left-tailed (\( H_1: \mu < \mu_0 \)), or right-tailed (\( H_1: \mu > \mu_0 \)). This calculator performs a two-tailed test.
- Test Statistic (Z): Calculated using the formula: \( Z = \frac{\bar{X} - \mu_0}{\frac{\sigma}{\sqrt{n}}} \), where \(\bar{X}\) is the sample mean, \(\mu_0\) is the hypothesized population mean, \(\sigma\) is the population standard deviation, and \(n\) is the sample size.
- P-value: The probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from a sample, under the assumption that the null hypothesis is true. A small p-value (typically ≤ α) suggests that the null hypothesis should be rejected.
- Significance Level (α): A threshold chosen by the researcher to decide whether to reject the null hypothesis. Common values are 0.01, 0.05, and 0.10.
Use this calculator to quickly perform a one-sample Z-test and understand whether your sample data provides enough evidence to reject the null hypothesis.