Example 1:
Find the minimum sample size required to estimate the prevalence of smoking with maximum absolute allowable error of 10, with confidence level of 95%. The expected prevalence in the population is 25%.
Solution:
Here
P = 25%, ε (absolute error) = 10, Confidence level = 95%
After putting these values, we get required sample size = 72
What will happen after selecting this sample size, considering that we get the prevalence = 25% as anticipated?
SE of proportion = SQRT (P * (1-P) / N) = SQRT (0.25 * 0.75 / 72 ) = 0.05
95 % CI of proportion = P ± 1.96 * SE
95% CI of proportion = 0.25 ± 1.96 * 0.05
95% CI of proportion = 0.15 to 0.35
95% CI of prevalence = 15 % to 35 %
(allowable error of 10 towards both sides of prevalence, at 95% confidence level)
Example 2:
Find the minimum sample size required to estimate the prevalence of smoking with maximum relative allowable error of 10% of its value, with confidence level of 95%. The expected prevalence in the population is 25%.
Solution:
Here
P = 25%, ε (relative error) = 10%, Confidence level = 95%
After putting these values, we get required sample size = 1152
What will happen after selecting this sample size, considering that we get the prevalence = 25% as anticipated?
SE of proportion = SQRT (P * (1-P) / N) = SQRT (0.25 * 0.75 / 1152 ) = 0.013
95 % CI of proportion = P ± 1.96 * SE
95% CI of proportion = 0.25 ± 1.96 * 0.0127
95% CI of proportion = 0.2250 to 0.2750
95% CI of prevalence = 22.50 % to 27.50 %
(relative allowable error of 10% towards both sides of prevalence, at 95% confidence level. Please note that relative error of 10%, with respect to expected prevalence of 25%, is equal to the absolute allowable error of 2.5.)
@ Sachin Mumbare