One Sample Z Test

One Sample Z Test

One Sample Z Test

Description

One-sample z-test is a statistical test used to determine if the mean of a single sample is significantly different, from a hypothesized population mean, when the population standard deviation is known. 

Why to use

Comparing sample mean to a known population mean 

When to use

  • Normally distributed population
  • Known Population Standard deviation

When not to use

  • Unknown population standard deviation
  • Small sample size
  • Non-normal population distribution

Prerequisites

  • Random sampling
  • Independence
  • Known population standard deviation
  • Large sample size 

Input

Any dataset containing numerical variables.

Output

It provides information about the statistical significance and confidence intervals associated with the test.

Statistical Methods Used

  • z-statistics
  • Calculate the p-value

Limitations

  • Normality assumption
  • Large sample size requirement
  • Sensitivity to outliers
  • Normality assumption
  • Limited scope


One sample z test is a statistical test to verify whether the sample mean differs from the population mean. This test is used when we know the population standard deviation.
The formula for one sample z-test is given below.

Where,
σ = Population Standard Deviation
n = Number of elements in Sample
μ = Sample mean

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