We run a hypothesis test that helps statisticians determine if the evidence are enough in a sample data to conclude that a research condition is true or false for the entire population. For finding out hypothesis of a given sample, we conduct a Z-test. Usually, in Hypothesis testing, we compare two sets by comparing against a synthetic data set and idealized model.

The Z test formula is given as:

$$z=\frac{\bar{x}-\mu }{\frac{\sigma }{\sqrt{n}}}$$

Where,

is the sample mean
is the population mean
is the standard deviation and n is the sample size.

Solved Examples

Question: What will be the z value when the given parameters are sample mean = 600, population mean = 585, the standard deviation is 100 and the sample size is 150?

Solution:

Given parameters are,
Sample mean,

= 600
Population mean, = 585,
Standard deviation, = 100
Sample size, n = 150

The formula for hypothesis testing is given as,

=1.837