Significance test

A Significance test aims to make a statement about a population parameter based on sample evidence.

Step	Example
1 State hypothesis	$H_{0}:\mu =\mu _{0}$
	$H_{0}:\mu \neq \mu _{0}$
2 State significance level	5%
3 State critical values
	1.96
4 Calculate test statistics	Varies per test
5 Compare the z-value to the critical values
6 Reach a conclusion
7 Put conclusion in English	The sample evidence does not support the claim that the population mean was the specified value

Given the following example: A production manager claims that 50 boxes per hour are filled with finished goods. A random sample of 48 different workers at different times shows an average of 47.5 with a standard deviation of 0.7 boxes. Does this data support evidence of the production managers claim? In this case a test for a population mean can look as follows

Step	Example
1 State hypthesis	$H_{0}:\mu =50$
	$H_{0}:\mu \neq 50$
2 State significance level	5%
3 State critical values
	1.96
4 Calculate test statistics	$z={\frac {47.5-50}{0.7/{\sqrt {47}}}}={\frac {-2.5}{0.101036}}=-24.744$
5 Compare the z-value to the critical values	The calculated value -24.744 is below the lower critical value -1.96
6 Reach a conclusion	We therefore reject the $H_{0}$ hypothesis at the 5% significant level
7 Put conclusion in English	The sample evidence does not support the claim that the population mean was the specified value. The number significantly different from 50

Part of M7-Quantitative Decision Methods-S4 - Significance Testing