Hypothesis Testing Formula

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:

\[\large z=\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}}\]

Where,
$\overline{x}$ is the sample mean
$\mu$ is the population mean
$\sigma$ 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, $\bar{x}$ = 600
Population mean, $\mu$ = 585,
Standard deviation, $\sigma$ = 100
Sample size, n = 150

The formula for hypothesis testing is given as,

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

$z=\frac{600-585}{\frac{100}{\sqrt{150}}}$

= 0.012

Practise This Question

Which of the following is an example of perpendicular lines?

1. Corners of your circular room floor

2. One of the angles in both your set squares

3. Angle included between the hour hand and minute hand when it is 12:15 in your wall clock

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