Hypothesis Testing Formula
A hypothesis testing formula is used to help statisticians determine if the available evidence is enough in a sample data to conclude that a research condition is true for the entire population or not. A ztest for finding out the hypothesis of a given sample. A zscore derived after running the ztest is a number representing the result from the ztest. Let us learn about the hypothesis testing formula in more detail.
What is the Hypothesis Testing Formula?
Usually, in hypothesis testing, we compare two sets by comparing against a reference data set and ideal model. Let's learn about the hypothesis testing formula. For finding out the hypothesis of a given sample, a ztest is conducted.
The ztest formula is given as:
\(z=\frac{\bar{x}\mu}{\frac{\sigma}{\sqrt{n}}}\)
Where,
 \(\bar{x}\) is the sample mean
 μ is the population mean
 σ is the standard deviation and n is the sample size.
Let us now look at a few solved examples on the hypothesis testing formula to understand the concept better.
Solved Examples Using Hypothesis Testing Formula

Example 1: Find the z value if the parameters are as follows: sample mean = 500, population mean = 485, the standard deviation is 90 and the sample size is 140?
Solution:
Sample mean, \(\bar{x} = 500\) Population mean, \(\mu = 485\), Standard deviation, \(\sigma = 90\) Sample size, \(n = 140\)
Using the hypothesis testing formula:
\(z=\frac{\bar{x}\mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z=\frac{500485}{\frac{90}{\sqrt{140}}}\)
\(=1.837\)Answer: z = 1.972

Example 2: What will be the z value if the parameters are as follows: sample mean = 800, the population mean = 785, the standard deviation is 100 and the sample size is 180?
Solution:
Sample mean, \(\bar{x} = 800\) Population mean, \(\mu = 785\), Standard deviation, \(\sigma = 100\) Sample size, \(n = 180\)
Using the hypothesis testing formula:
\(z=\frac{\bar{x}\mu}{\frac{\sigma}{\sqrt{n}}}\)
\(z=\frac{800785}{\frac{100}{\sqrt{180}}}\)
\(z=2.01\)Answer: z = 2.01