Difference between revisions of "Hypothesis Testing"
(→A ProblemM. K. Chung's lecture notes, 2003.) |
(→A ProblemM. K. Chung's lecture notes, 2003.) |
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<syntaxhighlight lang="r" line='line'> | <syntaxhighlight lang="r" line='line'> | ||
> x<-c(30, 25, 70, 110, 40, 80, 50, 60, 100, 60) | > x<-c(30, 25, 70, 110, 40, 80, 50, 60, 100, 60) | ||
− | |||
> mean(x) | > mean(x) | ||
[1] 62.5 | [1] 62.5 | ||
</syntaxhighlight> | </syntaxhighlight> | ||
+ | Since the average IQ of 10 dogs are lower than 100, one would be inclined to reject {{#tag:math|H_0}}. | ||
+ | Let {{#tag:math|X ̄}} be a test statistic and {{#tag:math|R = (−∞,90]}} to be a rejection region. Let’s compute the probability of making Type I error based on this testing procedure. Under the assumption {{#tag:math|H_0}} is true, | ||
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
[math]H_0 : \mu = 100 \text{vs.} H_1 : \mu \lt 100[/math].
One reasonable thing one may try is to see how high the sample mean is.
1 > x<-c(30, 25, 70, 110, 40, 80, 50, 60, 100, 60)
2 > mean(x)
3 [1] 62.5
Since the average IQ of 10 dogs are lower than 100, one would be inclined to reject [math]H_0[/math].
Let [math]X ̄[/math] be a test statistic and [math]R = (−∞,90][/math] to be a rejection region. Let’s compute the probability of making Type I error based on this testing procedure. Under the assumption [math]H_0[/math] is true,
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