how do i write this into a formula confide level 95% margin of error 5% population 10,000 sample size 370 like n= and so on i m not sure how to do that
To write this information into a formula, we can use the formula for calculating the sample size needed for estimating a population mean with a specified confidence level and margin of error. The formula is:
n = (Z^2 * p * (1-p))/(E^2)
Where:
n is the sample size,
Z is the Z-score corresponding to the desired confidence level,
p is the estimated population proportion,
1-p is the complement of the estimated population proportion,
E is the margin of error.
In your case, the given information is:
Confidence level: 95% (which corresponds to a Z-score of 1.96 for a large sample size)
Margin of error: 5% (0.05 in decimal form)
Population size: 10,000
Using the formula, we can calculate the sample size as follows:
n = (1.96^2 * 0.5 * 0.5) / (0.05^2)
n = (3.8416 * 0.25) / 0.0025
n = 0.9604 / 0.0025
n ≈ 384.16
Since the sample size should be a whole number, we round up the result to the nearest whole number:
n ≈ 385
Thus, the sample size needed to achieve a 95% confidence level with a 5% margin of error for a population of 10,000 is approximately 385.