a mean = 0.5, and the standard deviation is 1.84*10^-3 ( gassian statistic apply). How many replicated if the standard error of the mean is not excess 0.001%.
Please help, thank you so much
To find out how many replicates are needed, we first need to understand the relationship between standard error of the mean (SEM), the standard deviation (σ), and the sample size (n).
The formula for calculating SEM is:
SEM = σ / √n
Given that the SEM should not exceed 0.001% of the mean, we can write this condition as:
SEM ≤ 0.00001 * mean
Substituting the formula for SEM, we get:
σ / √n ≤ 0.00001 * mean
Now, we can rearrange the equation to solve for n:
σ / (0.00001 * mean) ≤ √n
Squaring both sides of the inequality will eliminate the square root:
(σ^2) / (0.0000000001 * mean^2) ≤ n
Substituting the given values from your question:
(1.84 * 10^-3)^2 / (0.0000000001 * 0.5^2) ≤ n
Evaluating the left side of the inequality:
0.0000033856 / 0.000000000025 ≤ n
Simplifying the left side:
135424 ≤ n
Therefore, to ensure that the standard error of the mean does not exceed 0.001%, you will need at least 135424 replicates.