Question

American Medical Association wants to estimate the proportion of medical doctors who had a solo practice. How many doctors should be included in the study if the association wants 99% confident that the estimate is within 5 percentage point of the true population proportion?

Answer 1

The number of doctors 'n' = 6.76

Explanation:

Explanation:-

Given Estimate of the true population proportion = 5 % = 0.05

Given level of significance ∝ = 99% or 1%

Z₀.₀₁ = 2.576

The margin of error is determined by

`M.E = (2.576 X √(p(1-p)) )/(√(n) )`

we know that
`√(p(1-p)) \leq (1)/(2)`

`0.05 = (2.576 X (1)/(2) )/(√(n) )`

Cross multiplication , we get

`√(n) = (2.576 X (1)/(2) )/(5)`

√n = 0.2576≅0.26

squaring on both sides,we get

n = 0.0676 X 100

n= 6.76

Final answer:-

The number of doctors 'n' = 6.76