Difference between revisions of "Hypothesis Testing"
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<center>H. Kemal Ilter<br>2020</center> | <center>H. Kemal Ilter<br>2020</center> | ||
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+ | ==Concepts== | ||
# 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}}. | # 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}}. | ||
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# 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. {{#tag:math|P(\text{Type I error}) = P(\text{reject }H_0 \mid H_0\text{ true}) = \alpha}}. The resulting {{#tag:math|\alpha}} is called the significance level of the test and the corresponding test is called a level {{#tag:math|\alpha}} test. We will use test procedures that give {{#tag:math|\alpha}} 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(\text{Type I error}) = P(\text{reject }H_0 \mid H_0\text{ true}) = \alpha}}. The resulting {{#tag:math|\alpha}} is called the significance level of the test and the corresponding test is called a level {{#tag:math|\alpha}} test. We will use test procedures that give {{#tag:math|\alpha}} less than a specified level (0.05 or 0.01). | ||
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+ | ==A Problem== | ||
{{References}} | {{References}} | ||
[[Category:Blog]] | [[Category:Blog]] |
References
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