Statistical Background on DOE - Revision history

Sharon Honecker: /* Inference on the Variances of Two Normal Populations */

2016-02-26T21:48:26Z

Inference on the Variances of Two Normal Populations

2016-01-06T21:43:19Z

Random Variables and the Normal Distribution

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	[[Image:doe31.png\|center\|~~400px~~\|Normal probability density functions for different values of mean and standard deviation.]]		[[Image:doe31.png\|center\|500px\|Normal probability density functions for different values of mean and standard deviation.\|link=]]


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	[[Image:doe32.png\|center\|~~450px~~\|Normal probability density function with the shaded area representing the probability of occurrence of data between 7 and 14 miles.]]		[[Image:doe32.png\|center\|550px\|Normal probability density function with the shaded area representing the probability of occurrence of data between 7 and 14 miles.\|link=]]

2016-01-06T21:42:47Z

Central Limit Theorem

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	[[Image:doe33.png\|center\|~~400px~~\|Sampling distribution of the sample mean. The distribution is normal with the mean equal to the population mean and the variance equal to the ''n''th fraction of the population variance.]]		[[Image:doe33.png\|center\|500px\|Sampling distribution of the sample mean. The distribution is normal with the mean equal to the population mean and the variance equal to the ''n''th fraction of the population variance.\|link=]]

	==Unbiased and Biased Estimators==		==Unbiased and Biased Estimators==

2016-01-06T21:42:24Z

Unbiased and Biased Estimators

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	[[Image:doe34.png\|center\|~~400px~~\|Example showing the distribution of a biased estimator which underestimated the parameter in question, along with the distribution of an unbiased estimator.]]		[[Image:doe34.png\|center\|500px\|Example showing the distribution of a biased estimator which underestimated the parameter in question, along with the distribution of an unbiased estimator.\|link=]]

2016-01-06T21:42:03Z

Standard Normal Distribution

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	[[Image:doe35.png\|center\|~~400px~~\|Standard normal distribution.]]		[[Image:doe35.png\|center\|500px\|Standard normal distribution.\|link=]]

	==Chi-Squared Distribution==		==Chi-Squared Distribution==

2016-01-06T21:41:45Z

Chi-Squared Distribution

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	[[Image:doe36.png\|center\|~~400px~~\|Chi-squared distribution.]]		[[Image:doe36.png\|center\|500px\|Chi-squared distribution.\|link=]]

2016-01-06T21:41:21Z

Student's t Distribution (t Distribution)

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	[[Image:doe37.png\|center\|~~400px~~\|<math>t\,\!</math> distribution.]]		[[Image:doe37.png\|center\|500px\|<math>t\,\!</math> distribution.\|link=]]

	==F Distribution==		==F Distribution==

2016-01-06T21:40:55Z

F Distribution

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	[[Image:doe38.png\|center\|~~400px~~\|<math>F\,\!</math> distribution.]]		[[Image:doe38.png\|center\|500px\|<math>F\,\!</math> distribution.\|link=]]

	=Hypothesis Testing=		=Hypothesis Testing=

2016-01-06T21:40:07Z

Hypothesis Testing

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	[[Image:doe39.png\|center\|~~400px~~\|Acceptance region and critical regions for the hypothesis test.]]		[[Image:doe39.png\|center\|500px\|Acceptance region and critical regions for the hypothesis test.\|link=]]

2016-01-06T21:39:41Z

Inference on the Mean of a Population When the Variance Is Known

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	[[Image:doe310.png\|center\|~~400px~~\|One-sided hypothesis where the critical region lies in the right tail.]]		[[Image:doe310.png\|center\|500px\|One-sided hypothesis where the critical region lies in the right tail.\|link=]]


	[[Image:doe311.png\|center\|~~400px~~\|One-sided hypothesis where the critical region lies in the left tail.]]		[[Image:doe311.png\|center\|500px\|One-sided hypothesis where the critical region lies in the left tail.\|link=]]


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	[[Image:doe312.png\|center\|~~400px~~\|Critical values and rejection region marked on the standard normal distribution.]]		[[Image:doe312.png\|center\|500px\|Critical values and rejection region marked on the standard normal distribution.\|link=]]