Re: [Boost-users] Confused with the example students_t_single_sample.cpp

Subject: Re: [Boost-users] Confused with the example students_t_single_sample.cpp
From: John Maddock (john_at_[hidden])
Date: 2014-01-15 13:18:12

Just to say I haven't forgotten this, will (hopefully!) get to it soon,

John.

> I got a problem with the example "students_t_single_sample.cpp".
> The corresponding document is at:
> http://www.boost.org/doc/libs/1_55_0/libs/math/doc/html/math_toolkit/stat_tut/weg/st_eg/tut_mean_test.html
>
> Actally, I am confused with the mathematical logic rather than coding.
> The document presents a table that shows four hypothesis and tests, I am 
> OK with the frist two,
> but for the third and the fourth ones:
>
> The original text:
> Hypothesis 3: the sample mean is less than the true mean
> Test 3: Reject if CDF of t > significance level, cdf(dist, t) > alpha
>
> I think p-value should be the integral from t to +Infinite: 
> cdf(complement(dist, t)),
> So reject Hypothesis 3 when  cdf(complement(dist, t)) < alpha, or say 
> cdf(dist, t) > 1-alpha
>
> The original text:
> Hypothesis 4: the sample mean is greater than the true mean
> Reject if complement of CDF of t > significance level: 
> cdf(complement(dist, t)) > alpha
>
> Similarly, the p-value should be the integral from -Infinite to t: 
> cdf(dist, t),
> so reject Hypothesis 4 when cdf(dist, t) < alpha
>
> Is that right?
> Thanks.
>
> Zhiyu Li
>
> 2014-01-11
>
>
>
> lizy10b
>

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