Significance test - Revision history

Dirkjan at 20:02, 27 August 2020

2020-08-27T20:02:45Z

Dirkjan: Replaced content with "Significance test Category:mbi Category:Decision Category:M7 Category:Methods Category:Quantitative Category:Term"

2020-08-27T19:21:12Z

Replaced content with "Significance test Category:mbi Category:Decision Category:M7 Category:Methods Category:Quantitative Category:Term"

Dirkjan: Created page with "A Significance test aims to make a statement about a population parameter based on sample evidence. {| class="wikitable" !Step !Example |- |1 State hypothesis | $H_0: \mu..."$

2020-08-25T08:06:43Z

Created page with "A Significance test aims to make a statement about a population parameter based on sample evidence. {| class="wikitable" !Step !Example |- |1 State hypothesis |<math>H_0: \mu..."

New page

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

{| class="wikitable"
!Step
!Example
|-
|1 State hypothesis
|<math>H_0: \mu=\mu_0</math>
|-
|
|<math>H_0: \mu\neq\mu_0</math>
|-
|2 State significance level
|5%
|-
|3 State critical values
|-1.96
|-
|
|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
{| class="wikitable"
!Step
!Example
|-
|1 State hypthesis
|<math> H_0: \mu=50</math>
|-
|
|<math> H_0: \mu\neq50</math>
|-
|2 State significance level
|5%
|-
|3 State critical values
|-1.96
|-
|
|1.96
|-
|4 Calculate test statistics
|<math>z=\frac {47.5 - 50}{0.7/\sqrt{47}} = \frac{-2.5}{0.101036} = -24.744</math>
|-
|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 <math>H_0</math> 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|M7-Quantitative Decision Methods-S4 - Significance Testing]]
[[Category:mbi]]

[[Category:Decision]]

[[Category:M7]]

[[Category:Methods]]

[[Category:Quantitative]]

[[Category:Term]]

← Older revision		Revision as of 19:21, 27 August 2020
Line 1:		Line 1:
−	A Significance test ~~aims to make a statement about a population parameter based on sample evidence.~~	+	Significance test
−
−	~~{\| class="wikitable"~~
−	~~!Step~~
−	~~!Example~~
−	\|-
−	~~\|1 State hypothesis~~
−	~~\|<math>H_0: \mu=\mu_0</math>~~
−	\|-
−	\|
−	~~\|<math>H_0: \mu\neq\mu_0</math>~~
−	\|-
−	~~\|2 State significance level~~
−	~~\|5%~~
−	\|-
−	~~\|3 State critical values~~
−	~~\|-1.96~~
−	\|-
−	\|
−	~~\|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
−	~~{\| class="wikitable"~~
−	~~!Step~~
−	~~!Example~~
−	\|-
−	~~\|1 State hypthesis~~
−	~~\|<math> H_0: \mu=50</math>~~
−	\|-
−	\|
−	~~\|<math> H_0: \mu\neq50</math>~~
−	\|-
−	~~\|2 State significance level~~
−	~~\|5%~~
−	\|-
−	~~\|3 State critical values~~
−	~~\|-1.96~~
−	\|-
−	\|
−	~~\|1.96~~
−	\|-
−	~~\|4 Calculate test statistics~~
−	~~\|<math>z=\frac {47.5 - 50}{0.7/\sqrt{47}} = \frac{-2.5}{0.101036} = -24.744</math>~~
−	\|-
−	~~\|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 <math>H_0</math> 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\|M7-Quantitative Decision Methods-S4 - Significance Testing]]~~
	[[Category:mbi]]		[[Category:mbi]]

← Older revision		Revision as of 20:02, 27 August 2020
Line 1:		Line 1:
−	Significance test	+	A Significance test aims to make a statement about a population parameter based on sample evidence.
		+
		+	{\| class="wikitable"
		+	!Step
		+	!Example
		+	\|-
		+	\|1 State hypothesis
		+	\|<math>H_0: \mu=\mu_0</math>
		+	\|-
		+	\|
		+	\|<math>H_0: \mu\neq\mu_0</math>
		+	\|-
		+	\|2 State significance level
		+	\|5%
		+	\|-
		+	\|3 State critical values
		+	\|-1.96
		+	\|-
		+	\|
		+	\|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
		+	{\| class="wikitable"
		+	!Step
		+	!Example
		+	\|-
		+	\|1 State hypthesis
		+	\|<math> H_0: \mu=50</math>
		+	\|-
		+	\|
		+	\|<math> H_0: \mu\neq50</math>
		+	\|-
		+	\|2 State significance level
		+	\|5%
		+	\|-
		+	\|3 State critical values
		+	\|-1.96
		+	\|-
		+	\|
		+	\|1.96
		+	\|-
		+	\|4 Calculate test statistics
		+	\|<math>z=\frac {47.5 - 50}{0.7/\sqrt{47}} = \frac{-2.5}{0.101036} = -24.744</math>
		+	\|-
		+	\|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 <math>H_0</math> 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\|M7-Quantitative Decision Methods-S4 - Significance Testing]]
	[[Category:mbi]]		[[Category:mbi]]

Significance test - Revision history

Dirkjan at 20:02, 27 August 2020

Dirkjan: Replaced content with "Significance test Category:mbi Category:Decision Category:M7 Category:Methods Category:Quantitative Category:Term"

Dirkjan: Created page with "A Significance test aims to make a statement about a population parameter based on sample evidence. {| class="wikitable" !Step !Example |- |1 State hypothesis |H_0: \mu..."

Dirkjan: Created page with "A Significance test aims to make a statement about a population parameter based on sample evidence. {| class="wikitable" !Step !Example |- |1 State hypothesis | $H_0: \mu..."$