Difference between revisions of "Hypothesis Testing"

Revision as of 08:29, 16 November 2020

H. Kemal Ilter
2020

The null hypothesis [math]H_0[/math] is a claim about the value of a population parameter. The alternate hypothesis [math]H_1[/math] is a claim opposite to [math]H_0[/math].
A test of hypothesis is a method for using sample data to decide whether to reject [math]H_0[/math]. [math]H_0[/math] will be assumed to be true until the sample evidence suggest otherwise.
A test statistic is a function of the sample data on which the decision is to be based.
A rejection region is the set of all values of a test statistic for which [math]H_0[/math] is rejected.
Type I error: you reject [math]H_0[/math] when [math]H_0[/math] is true. [math]P (Type I error) = P (reject H0[/math]. The resulting α is called the significance level of the test and the corresponding test is called a level α test. We will use test procedures that give α less than a specified level (0.05 or 0.01).

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 # The ''null hypothesis'' {{#tag:math|H_0}} is a claim about the value of a population parameter. The ''alternate hypothesis'' {{#tag:math|H_1}} is a claim opposite to {{#tag:math|H_0}}.
-# A test of hypothesis is a method for using sample data to decide whether to reject {{#tag:math|H_0}}. {{#tag:math|H_0}} will be assumed to be true until the sample evidence suggest otherwise.
+# A ''test of hypothesis'' is a method for using sample data to decide whether to reject {{#tag:math|H_0}}. {{#tag:math|H_0}} will be assumed to be true until the sample evidence suggest otherwise.
-# A test statistic is a function of the sample data on which the decision is to be based.
+# A ''test statistic'' is a function of the sample data on which the decision is to be based.
-# A rejection region is the set of all values of a test statistic for which {{#tag:math|H_0}} is rejected.
+# A ''rejection region'' is the set of all values of a test statistic for which {{#tag:math|H_0}} is rejected.
-# Type I error: you reject {{#tag:math|H_0}} when {{#tag:math|H_0}} is true. P (Type I error) = P (reject H0|H0 true) = α. The resulting α is called the significance level of the test and the corresponding test is called a level α test. We will use test procedures that give α less than a specified level (0.05 or 0.01).
+# ''Type I error'': you reject {{#tag:math|H_0}} when {{#tag:math|H_0}} is true. {{#tag:math|P (Type I error) = P (reject H0|H0 true) = α}}. The resulting α is called the significance level of the test and the corresponding test is called a level α test. We will use test procedures that give α less than a specified level (0.05 or 0.01).
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