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We have a contest 1 weeks ago. One question is a bit strange for us as follows:

$X\sim B(4,p). $ for test $H_0:p=0.2$ versus $H_1:p>0.2$. if $X=4$, $H_0$ assumption is rejected. calculate type I error‌‌?

is there any hint by expert, how we can solve this contest question ?

Answer from sheet: 0.0016

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Type-I error is a type of error that occurs when a null hypothesis is rejected although it is true(i.e. $P(reject H_0|H_0)$)

Read more: http://www.investopedia.com/terms/t/type_1_error.asp#ixzz3XfOLYrFdr

As we reject $H_0$ only when X=4 and p=0.2 when $H_0$ is true,

Type-I error =$P(reject H_0|H_0)=P(X=4|p=0.2)=\binom{4}{0}0.2^4*0.8^0=0.0016$

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    $\begingroup$ would you please more describe ? $\endgroup$
    – user72371
    Apr 18, 2015 at 13:15
  • $\begingroup$ is it understandable? $\endgroup$ Apr 18, 2015 at 13:23
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    $\begingroup$ It's not bad to add some detail on your answer for other reader :) but nice answer +1 $\endgroup$ Apr 18, 2015 at 13:56
  • $\begingroup$ I edited with pleasure! :) $\endgroup$ Apr 18, 2015 at 15:14

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