Question

(7) The proportion of medical providers that adopt best opioid prescribing practices af- ter an educational program intervention is thought to be between 0.3 and 0.7. (a) How large a sample of medical providers is required to estimate the true proportion that adopt best practices after an educational intervention within 2.5 percentage points (£0.025) with 90% confidence. (b) How large a sample of medical providers is required to estimate the true mean that adopt best practices after an educational intervention within 2.5 percentage points (0.025) with 90% confidence and standard deviation 20 for all medical providers with best practices.

Answer 1

7.

a.
Given data,
sample proportion is between 0.3 and 0.7 = 0.5
confidence level is 90%
margin of error 2.5%
Compute Sample Size ( n ) = n=(Z/E)^2*p*(1-p)
Z a/2 at 0.1 is = 1.645
Sample Proportion = 0.5
ME = 0.025
n = ( 1.645 / 0.025 )^2 * 0.5*0.5
= 1082.41 ~ 1083          
b.
given data,
margin of error = 2.5%
confidence level is 90%
standard deviation is 20
Compute Sample Size
n = (Z a/2 * S.D / ME ) ^2
Zα/2 at 0.1% LOS is = 1.645 ( From Standard Normal Table )
Standard Deviation ( S.D) = 20
ME =0.025
n = ( 1.645*20/0.025) ^2
= (32.9/0.025 ) ^2
= 1731856 ~ 1731857