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Statistical Significance Formula

Statistical hypothesis testing is the a result that is attained when a p – value is lesser than the significance level, denoted by , alpha.   p – value is the probability of getting at least as extreme results that is provided that the null hypothesis is true. Statistical significance is the mean to get sure that the statistic is reliable.

If there is a large sample size, then small difference in the research findings can be negligible if you are very sure that the differences did not arise out of fluke. This formula helps us determine that there is a relationship in the differences or variations. Depending upon the sample size, to know how moderate, weak or strong is the relationship, statistical significance is used.

Statistical significance is also referred to as type 1 error. The formula and terminologies related to this formula is given as:

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

Solved Examples

Question:  Find out the statistical significance using the z test if the sample mean is 16, is $\mu$ 12, σ is 4 and the sample size is 30?

Solution

Given parameters are

$\overline{x}=15$
$\mu =12$
$\sigma =4$
$n = 30$

With the formula we can say that: $ Z=\frac{\overline{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$Z=\frac{15-12}{\frac{5}{\sqrt{30}}}$

$=\frac{3}{0.73}$

$=4.10$