Suppose a study is proposed to compare a renovascular procedure versus medical therapy in lowering the systolic blood pressure of patients with hypertension secondary to renal artery stenosis. on the basis of results of preliminary studies, the investigators estimate that the vascular procedure may lower blood pressure by 20 mm hg, while medical therapy may lower blood pressure by only 10 mm hg. on the basis of results of preliminary studies, the sd for blood pressure lowering is estimated to be 15 mm hg. a significance criterion of 0 .05 and power of 0.80 are chosen. if they want to do a two-sided test of equal population means with α= 0.05 and β= 0.20, what sample size should they use?

To understand the electric potential and electric field of a point charge in three dimensions consider a positive point charge q, located at the origin of three-dimensional space. throughout this problem, use k in place of 14? ? 0. part adue to symmetry, the electric field of a point charge at the origin must point from the origin.answer in one word.part bfind e(r), the magnitude of the electric field at distance r from the point charge q.express your answer in terms of r, k, and q. part cfind v(r), the electric potential at distance rfrom the point charge q.express your answer in terms of r, k, and q part dwhich of the following is the correct relationship between the magnitude of a radial electric field and its associated electric potential ? more than one answer may be correct for the particular case of a point charge at the origin, but you should choose the correct general relationship. a)e(r)=dv(r)drb)e(r)=v(r)rc)e(r)=? dv(r)drd)e(r)=? v(r)r