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

Subject: [Boost-users] Confused with the example students_t_single_sample.cpp
From: lizy10b (lizy10b_at_[hidden])
Date: 2014-01-10 22:58:03

Hi there,
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