What is minimum sample needed if you know the SD is 22.36 and an accuracy of 3.06 and you want a confidence level of 90%
To determine the minimum sample size needed with a known standard deviation, desired level of accuracy, and a specified confidence level, you can use the formula for sample size calculation:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score (corresponding to the desired confidence level)
σ = population standard deviation
E = desired level of accuracy (also known as the margin of error)
In your case, the given information is:
σ (population standard deviation) = 22.36
E (desired level of accuracy) = 3.06
Confidence level = 90% (which corresponds to a Z-score of 1.645)
Plugging these values into the formula, you can calculate the minimum sample size:
n = (1.645 * 22.36 / 3.06)^2
n = 11.979^2
n ≈ 143.6
Therefore, the minimum sample size needed to achieve a 90% confidence level, given a standard deviation of 22.36 and an accuracy of 3.06, is approximately 144.