Question

A medical resident doing research wants to know if the mean heart rate after a particular type of trauma differs from the healthy population rate of 72 beats/min. They consider a mean difference of 6 beats/min to be clinically meaningful. They also choose 9.1 beats/min as the variation based on a previously published study. How many patients will be needed to carry out the study at 0.0005% significance and 82% power?

Answer 1

Level of Significance ,    α =    0.000005

power = 0.82
ß= 1-power = 0.18

δ=   µ - µo =    6

std dev =    σ =    9.1

two tailed test

Z (α/2)=       4.5648   [excel function: =normsinv(α/2)
          
Z (ß) =        0.9154   [excel function: =normsinv(ß)

sample size needed =    n = ( σ [ Z(ß)+Z(α/2) ] / δ )² = (9.1*(0.9154 + 4.5648)/6 )² = 69.0821

so, sample size =        70