TATITIC CALCULATOR
Z Test
A precise tool.
What is the Z Test & How does it work?
The oneβsample Z test is used when the population standard deviation is known and the sample size is large enough for the Central Limit Theorem to apply. It compares the sample mean to a hypothesized population mean and expresses the difference in units of standard error, producing a Zβstatistic that follows the standard normal distribution under the null hypothesis. If the absolute Z exceeds the critical value for the chosen significance level, the null hypothesis is rejected.
Z = frac{bar{x} – mu_{0}}{sigma / sqrt{n}}
Z = test statistic
Parameters
Result
β
Frequently Asked Questions
When should I use the Z Test Calculator?
Use it when you have a large sample size and know the population standard deviation.
What does the Z-statistic tell me?
The Z-statistic tells you how many standard errors your sample mean is from the hypothesized population mean.
How do I interpret the results of a Z Test?
If the absolute value of the Z-statistic exceeds the critical value for your chosen significance level, reject the null hypothesis.
What is the Central Limit Theorem in this context?
The Central Limit Theorem allows us to assume that the sample mean follows a normal distribution if the sample size is large enough.
Can I use this calculator for small samples?
No, this calculator is for large samples where the Central Limit Theorem applies. For small samples, consider using a t-test instead.
What is the null hypothesis in a Z Test?
The null hypothesis states that there is no difference between the sample mean and the hypothesized population mean.
How do I find the critical value for my Z Test?
Look up the critical value in a standard normal distribution table based on your chosen significance level and whether it’s a one-tailed or two-tailed test.
Results are for informational purposes only and do not constitute professional advice.