Standard error - Revision history

Dirkjan at 20:03, 27 August 2020

2020-08-27T20:03:17Z

Dirkjan: Replaced content with "Standard error Category:mbi Category:Decision Category:M7 Category:Methods Category:Quantitative Category:Term"

2020-08-27T19:21:33Z

Replaced content with "Standard error Category:mbi Category:Decision Category:M7 Category:Methods Category:Quantitative Category:Term"

Dirkjan: Created page with "The standard error of the mean of a sample from a population is defined as: $\frac{\sigma_X}{\sqrt{n}}$ is (an estimation of) the standard deviation of $X$
2020-08-25T08:07:13Z

Created page with "The standard error of the mean of a sample from a population is defined as: <math>\frac{\sigma_X}{\sqrt{n}}</math> is (an estimation of) the standard deviation of <math>X</ma..."

New page
The standard error of the mean of a sample from a population is defined as:

<math>\frac{\sigma_X}{\sqrt{n}}</math> is (an estimation of) the standard deviation of <math>X</math> and is called the '''[[Standard error|Standard error]]'''. As example imaging that the time spend in traffic by employees has a mean of 60 and a standard deviation of 20. If employees are selected at random, what is the probability that the sample average will be over 64 minutes if the sample size is (a) 40 or (b) 100.

a) With sample of 40 we have:
standard error = <math>\frac{20}{\sqrt 40}</math> = 3.162278
and
Z = <math>\frac {X-\mu}{\sigma}</math> = <math>\frac {64-60}{3.162278}</math> = 1.2649
Looking up this value in [[Standard Normal Distribution Table|Standard Normal Distribution Table]] we find a value of 1 - 0.5 - 0.3962 = 0.1038 (~10%)

b) With sample of 100 we have:
standard error = <math>\frac{20}{\sqrt 100}</math> = 2
and
Z = <math>\frac {X-\mu}{\sigma}</math> = <math>\frac {64-60}{2}</math> = 2
Looking up this value in [[Standard Normal Distribution Table|Standard Normal Distribution Table]] we find a value of 1 - 0.5 - 0.4772 = 0.0228 (~2%)

Part of: [[M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals|M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals]]
Seel also: http://en.wikipedia.org/wiki/Standard_error_%28statistics%29
[[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:
−	~~The standard error of the mean of a sample from a population is defined as:~~	+	Standard error
−
−	~~<math>\frac{\sigma_X}{\sqrt{n}}</math> is (an estimation of) the standard deviation of <math>X</math> and is called the '''[[~~Standard error\|Standard error]]'''. As example imaging that the time spend in traffic by employees has a mean of 60 and a standard deviation of 20. If employees are selected at random, what is the probability that the sample average will be over 64 minutes if the sample size is (a) 40 or (b) 100.
−
−	~~a) With sample of 40 we have:~~
−	~~standard error = <math>\frac{20}{\sqrt 40}</math> = 3.162278~~
−	~~and~~
−	~~Z = <math>\frac {X-\mu}{\sigma}</math> = <math>\frac {64-60}{3.162278}</math> = 1.2649~~
−	~~Looking up this value in [[Standard Normal Distribution Table\|Standard Normal Distribution Table]] we find a value of 1 - 0.5 - 0.3962 = 0.1038 (~10%)~~
−
−	~~b) With sample of 100 we have:~~
−	~~standard error = <math>\frac{20}{\sqrt 100}</math> = 2~~
−	~~and~~
−	~~Z = <math>\frac {X-\mu}{\sigma}</math> = <math>\frac {64-60}{2}</math> = 2~~
−	~~Looking up this value in [[Standard Normal Distribution Table\|Standard Normal Distribution Table]] we find a value of 1 - 0.5 - 0.4772 = 0.0228 (~2%)~~
−
−	~~Part of: [[M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals\|M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals]]~~
−	~~Seel also: http://en.wikipedia.org/wiki/Standard_error_%28statistics%29~~
	[[Category:mbi]]		[[Category:mbi]]

← Older revision		Revision as of 20:03, 27 August 2020
Line 1:		Line 1:
−	Standard error	+	The standard error of the mean of a sample from a population is defined as:
		+
		+	<math>\frac{\sigma_X}{\sqrt{n}}</math> is (an estimation of) the standard deviation of <math>X</math> and is called the '''[[Standard error\|Standard error]]'''. As example imaging that the time spend in traffic by employees has a mean of 60 and a standard deviation of 20. If employees are selected at random, what is the probability that the sample average will be over 64 minutes if the sample size is (a) 40 or (b) 100.
		+
		+	a) With sample of 40 we have:
		+	standard error = <math>\frac{20}{\sqrt 40}</math> = 3.162278
		+	and
		+	Z = <math>\frac {X-\mu}{\sigma}</math> = <math>\frac {64-60}{3.162278}</math> = 1.2649
		+	Looking up this value in [[Standard Normal Distribution Table\|Standard Normal Distribution Table]] we find a value of 1 - 0.5 - 0.3962 = 0.1038 (~10%)
		+
		+	b) With sample of 100 we have:
		+	standard error = <math>\frac{20}{\sqrt 100}</math> = 2
		+	and
		+	Z = <math>\frac {X-\mu}{\sigma}</math> = <math>\frac {64-60}{2}</math> = 2
		+	Looking up this value in [[Standard Normal Distribution Table\|Standard Normal Distribution Table]] we find a value of 1 - 0.5 - 0.4772 = 0.0228 (~2%)
		+
		+	Part of: [[M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals\|M7-Quantitative Decision Methods-S3 - Normal Distribution and confidence intervals]]
		+	Seel also: http://en.wikipedia.org/wiki/Standard_error_%28statistics%29
	[[Category:mbi]]		[[Category:mbi]]