The doctor want to know the effect of reducing blood pressure for a new medicine, chose 28 hypertensive patients to divide two groups randomly, one group as trial, another as control. the trial use the new medicine, the control use the standard medicine. measured the Diastolic Blood Pressure(DBP)mmHg before and after treatment, and calculated the reduce DBP values, see table 1.

Question

(1). Please make a statistical table according to the information above the material.
(2). Is the new medicine different from the standard medicine for the effect of reducing blood pressure ? Please make a statistical inference to judge.

table 1. the reduce DBP(mmHg) of before and after treatment for two medicines
no 1 2 3 4 5 6 7 8 9 10 11 12 13 14
trial 12 10 7 8 4 5 16 18 11 13 4 8 14 14
control -2 9 10 5 0 -2 10 -8 4 1 12 -3 4 5

Answer 1

Here we have two samples from two populations and would like to determine if the means are the same, namely to accept or reject:
H0: μ1-μ2=0

The sample size n=14 is not sufficient to justify normality using the central limit theorem. Either an assumption of normality has to be made, or a probability plot made to that end.
(for probability plots, see for example:
http://www.itl.nist.gov/div898/handbook/eda/section3/normprpl.htm
or
http://mathematiques.brinkster.net/probability/probabilityPlot.html
)

There is no reason to assume σ1=σ2, so assumption of inequality of σ would be justified.

The t-distribution does not describe exactly the situation, but for the current case of σ1≠σ2, an approximate statistic may be used:
To^*=(X̄1-X̄2-0)/√( S1²/n1 + S2²/n2 )

where ν, the degree of freedom for n=n1=n2=14 would be given by
ν=(n-1)[(S1+S2)²]/(S1²+s2²)

Typically two-tailed α=0.05 would be used, but do state the assumption of α.