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,

\(\begin{array}{l}\overline{x}\end{array} \)
is the sample mean
\(\begin{array}{l}\mu\end{array} \)
is the population mean
\(\begin{array}{l}\sigma\end{array} \)
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,

\(\begin{array}{l}\bar{x}\end{array} \)
= 600
Population mean,
\(\begin{array}{l}\mu\end{array} \)
= 585,
Standard deviation,
\(\begin{array}{l}\sigma\end{array} \)
= 100
Sample size, n = 150

The formula for hypothesis testing is given as,

\(\begin{array}{l}z=\frac{\overline{x}-\mu }{\frac{\sigma }{\sqrt{n}}}\end{array} \)

\(\begin{array}{l}z=\frac{600-585}{\frac{100}{\sqrt{150}}}\end{array} \)

=1.837

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