Difference between revisions of "Hypothesis Testing"
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# ''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). | ||
− | ==A Problem== | + | ==A Problem<ref>M. K. Chung's lecture notes, 2003.</ref>== |
+ | |||
+ | I believe that dogs are as smart as people. Assume IQ of a dog follows {{#tag:math|Xi \sim N(\mu,102)}}. IQ of 10 dogs are measured: 30, 25, 70, 110, 40, 80, 50, 60, 100, 60. We want to test if dogs are as smart as people by testing | ||
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+ | H0 :μ=100vs. H1 :μ<100. | ||
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+ | One reasonable thing one may try is to see how high the sample mean is. | ||
{{References}} | {{References}} | ||
[[Category:Blog]] | [[Category:Blog]] |
I believe that dogs are as smart as people. Assume IQ of a dog follows [math]Xi \sim N(\mu,102)[/math]. IQ of 10 dogs are measured: 30, 25, 70, 110, 40, 80, 50, 60, 100, 60. We want to test if dogs are as smart as people by testing
H0 :μ=100vs. H1 :μ<100.
One reasonable thing one may try is to see how high the sample mean is.
References
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