I need help with this I already did it on a calculator but now I don't know how to write the formula out on paper like n= for the population and * this or that I m not sure how to write it out help please
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 the formula for determining the sample size (n) of a population with a desired confidence level (C), margin of error (E), and known population size (N), you can use the following formula:
n = (Z^2 * p * (1 - p)) / (E^2)
Here's how you can fill in the values for your specific example:
1. Confidence Level (C): The confidence level is typically expressed as a percentage. In your case, the confidence level is 95%, so you can convert it to a decimal by dividing it by 100: C = 0.95.
2. Margin of Error (E): The margin of error represents the maximum allowable difference between the true population parameter and the sample estimate. In your case, the margin of error is 5%, so you also need to convert it to a decimal: E = 0.05.
3. Population Size (N): The population size is the total number of individuals in the population you're studying. In your case, the population size is 10,000: N = 10,000.
By substituting these values into the formula, you can calculate the sample size (n):
n = (Z^2 * p * (1 - p)) / (E^2)
To compute n, you'll first need to determine the value of Z, which represents the standard score associated with the desired confidence level. For a 95% confidence level, the corresponding Z-value is 1.96.
Next, you'll need to estimate the value of p, which represents the estimated proportion of the population that possesses the characteristic of interest. Since there's no specific value provided for p, and it's usually unknown in situations like this, you can use a conservative estimate of p = 0.5, which represents the highest variability (greatest sample size).
Once you have these values, you can plug them into the formula:
n = (1.96^2 * 0.5 * (1 - 0.5)) / (0.05^2)
Simplifying the equation:
n = (3.8416 * 0.25) / 0.0025
n ≈ 3841.6 / 0.0025
n ≈ 1,536,640
Therefore, the estimated sample size (n) needed to achieve a 95% confidence level, a 5% margin of error, and a population size of 10,000 is approximately 1,537 individuals.