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| − | A Significance test aims to make a statement about a population parameter based on sample evidence.
| + | Significance test |
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| − | {| class="wikitable"
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| − | !Step
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| − | !Example
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| − | |1 State hypothesis
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| − | |<math>H_0: \mu=\mu_0</math>
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| − | |<math>H_0: \mu\neq\mu_0</math>
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| − | |2 State significance level
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| − | |5%
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| − | |3 State critical values
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| − | |-1.96
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| − | |1.96
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| − | |4 Calculate test statistics
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| − | |Varies per test
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| − | |5 Compare the z-value to the critical values
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| − | |6 Reach a conclusion
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| − | |7 Put conclusion in English
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| − | |The sample evidence does not support the claim that the population mean was the specified value
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| − | |}
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| − | 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
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| − | {| class="wikitable"
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| − | !Step
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| − | !Example
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| − | |1 State hypthesis
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| − | |<math> H_0: \mu=50</math>
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| − | |<math> H_0: \mu\neq50</math>
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| − | |2 State significance level
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| − | |5%
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| − | |3 State critical values
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| − | |-1.96
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| − | |1.96
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| − | |4 Calculate test statistics
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| − | |<math>z=\frac {47.5 - 50}{0.7/\sqrt{47}} = \frac{-2.5}{0.101036} = -24.744</math>
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| − | |5 Compare the z-value to the critical values
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| − | |The calculated value -24.744 is below the lower critical value -1.96
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| − | |6 Reach a conclusion
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| − | |We therefore reject the <math>H_0</math> hypothesis at the 5% significant level
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| − | |7 Put conclusion in English
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| − | |The sample evidence does not support the claim that the population mean was the specified value. The number significantly different from 50
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| − | |}
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| − | Part of [[M7-Quantitative Decision Methods-S4 - Significance Testing|M7-Quantitative Decision Methods-S4 - Significance Testing]]
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| | [[Category:mbi]] | | [[Category:mbi]] |
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