Z-Test Calculator
Test whether a sample mean differs significantly from a known population mean.
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Enter the sample mean, population mean (null hypothesis value), known population standard deviation, and sample size. The calculator computes the z-statistic and two-tailed p-value. Use this when the population standard deviation is known.
About This Calculator
The z-test is a hypothesis test for comparing a sample mean to a known population mean when the population standard deviation is known. The test statistic z = (sample mean - population mean) / (sigma / sqrt(n)) follows the standard normal distribution. It is appropriate for large samples or when sigma is truly known.
Frequently Asked Questions
When should I use a z-test instead of a t-test?
Use a z-test only when the population standard deviation (sigma) is known. In practice, this is rare, and most situations call for a t-test instead.
What is a large enough sample for the z-test?
If the population is normal, any sample size works with a known sigma. If the population is non-normal, the Central Limit Theorem suggests n >= 30 for the sampling distribution to be approximately normal.
How do I interpret the z-statistic?
The z-statistic tells you how many standard errors the sample mean is from the hypothesized population mean. Values beyond +/-1.96 are significant at the 5% level.