Z-tests for Hypothesis testing: Formula & Examples

January 31, 2022 by Ajitesh Kumar · Leave a comment
Different types of Z-test - One sample and two samples

Z-tests are statistical hypothesis testing techniques that are used to determine whether the null hypothesis relating to comparing sample means or proportions with that of population at a given significance level can be rejected or otherwise based on the z-statistics or z-score. As a data scientist, you must get a good understanding of the z-tests and its applications to test the hypothesis for your statistical models. In this blog post, we will discuss an overview of different types of z-tests and related concepts with the help of examples. You may want to check my post on hypothesis testing titled – Hypothesis testing explained with examples

What are Z-tests & Z-statistics?

Z-tests can be defined as statistical hypothesis testing techniques that are used to quantify the hypothesis testing related to claim made about the population parameters such as mean and proportion. Z-test uses the sample data to test the hypothesis about the population parameters (mean or proportion). There are different types of Z-tests which are used to estimate the population mean or proportion, or, perform hypotheses testing related to samples’ means or proportions.

Different types of Z-tests 

There are following different types of Z-tests which are used to perform different types of hypothesis testing.  

Different types of Z-test - One sample and two samples

Four variables are involved in the Z-test for performing hypothesis testing for different scenarios. They are as follows:

  • An independent variable that is called the “sample” and assumed to be normally distributed;
  • A dependent variable that is known as the test statistic (Z) and calculated based on sample data
  • Different types of Z-test that can be used for performing hypothesis testing
  • A significance level or “alpha” is usually set at 0.05 but can take the values such as 0.01, 0.05, 0.1

When to use Z-test – Explained with examples

The following are different scenarios when Z-test can be used:

  • Compare the sample or a single group with that of the population with respect to the parameter, mean. This is called as one-sample Z-test for means. For example, whether the student of a particular school has been scoring marks in Mathematics which is statistically significant than the other schools. This can also be thought of as a hypothesis test to check whether the sample belongs to the population or otherwise.
  • Compare two groups with respect to the population parameter, mean. This is called as two-samples Z-test for means. For example, you want to compare class X students from different schools and determine if students of one school are better than others based on their score of Mathematics.
  • Compare hypothesized proportion of the population to that of population theoritical proportion. For example, whether the unemployment rate of a given state is different than the well-established rate for the ccountry
  • Compare the proportion of one population with the proportion of othe rproportion. For example, whether the efficacy rate of vaccination in two different population are statistically significant or otherwise.

Z-test Interview Questions 

Here is a list of a few interview questions you may expect in your data scientists interview:

  • What is Z-test?
  • What is Z-statistics or Z-score?
  • When to use Z-test vs other tests such as T-test or Chi-square test?
  • What is Z-distribution?
  • What is the difference between Z-distribution and T-distribution?
  • What is sampling distribution?
  • What are different types of Z-tests?
  • Explain different types of Z-tests with the help of real-world examples?
  • What’s the difference two samples Z-test for means and two-samples Z-test for proportions? Explain with one example each.
  • As data scientists, give some scenarios when you would like to use Z-test when building machine learning models?
Ajitesh Kumar
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Ajitesh Kumar

I have been recently working in the area of Data analytics including Data Science and Machine Learning / Deep Learning. I am also passionate about different technologies including programming languages such as Java/JEE, Javascript, Python, R, Julia, etc, and technologies such as Blockchain, mobile computing, cloud-native technologies, application security, cloud computing platforms, big data, etc. I would love to connect with you on Linkedin. Check out my latest book titled as First Principles Thinking: Building winning products using first principles thinking.
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