the director wants you to determine the true frequency for mass drug administration and coverage in the study area in which will yield the desired results. from literature, it is discovered that 75% coverage has always been achieved. the director wants a 95% confidence limit. (I)calculate the required sample size, if the desired precision is 4% of the true value (ii) what would be the sample size if the relative precision of +/-10% of the analyzed population proportion or 80%, with a design effect of 2, is envisaged. (iii) from (I) above, adjust for finite population in the study area of about 17 950 inhabitants
Question
the director wants you to determine the true frequency for mass drug administration and coverage in the study area in which will yield the desired results. from literature, it is discovered that 75% coverage has always been achieved. the director wants a 95% confidence limit. (I)calculate the required sample size, if the desired precision is 4% of the true value (ii) what would be the sample size if the relative precision of +/-10% of the analyzed population proportion or 80%, with a design effect of 2, is envisaged. (iii) from (I) above, adjust for finite population in the study area of about 17 950 inhabitants
Solution
(i) To calculate the required sample size with a desired precision of 4% of the true value, we use the formula for sample size in a proportion:
n = (Z^2 * P * (1-P)) / E^2
where:
- Z is the z-value (which is 1.96 for a 95% confidence level)
- P is the estimated proportion of the population which has the characteristic being measured (in this case, 75% or 0.75)
- E is the desired precision (in this case, 4% or 0.04)
Substituting the values into the formula, we get:
n = (1.96^2 * 0.75 * (1-0.75)) / 0.04^2 n = 441
So, the required sample size is approximately 441.
(ii) If the relative precision of +/-10% of the analyzed population proportion or 80%, with a design effect of 2, is envisaged, we use the same formula but with different values for P and E. In this case, P is 80% or 0.8 and E is 10% of P, which is 0.08. The design effect (DEFF) is also taken into account by multiplying the sample size by the DEFF.
n = (Z^2 * P * (1-P)) / E^2 * DEFF n = (1.96^2 * 0.8 * (1-0.8)) / 0.08^2 * 2 n = 768
So, the required sample size is approximately 768.
(iii) To adjust for a finite population (in this case, 17,950 inhabitants), we use the formula for the finite population correction factor:
n_adj = n / (1 + (n - 1) / N)
where:
- n is the sample size calculated in (i) (441)
- N is the population size (17,950)
Substituting the values into the formula, we get:
n_adj = 441 / (1 + (441 - 1) / 17950) n_adj = 438
So, the adjusted sample size is approximately 438.
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