If you want to be 95% confident of estimating the population proportion to within a sampling error of and there is historical evidence that the population proportion is approximately 0.40, what sample size is needed?
Formula to find sample size:
n = [(z-value)^2 * p * q]/E^2
... where n = sample size, z-value is 1.96, p = .4, q = 1 - p, ^2 means squared, * means to multiply, and E = ? (missing in problem).
Plug values into the formula and calculate n.
I hope this will help get you started.
To determine the sample size needed to estimate a population proportion with a desired level of confidence and margin of error, you can use the formula for sample size determination:
n = (Z^2 * p * (1-p)) / E^2,
where:
- n is the required sample size
- Z is the standard score corresponding to the desired level of confidence (in this case, 95% confidence corresponds to a Z-score of approximately 1.96)
- p is the estimated population proportion (0.40 in this case)
- E is the desired margin of error (sampling error)
Plugging in the values into the formula:
n = (1.96^2 * 0.40 * (1-0.40)) / (E^2).
As the desired margin of error is not specified in your question, you need to define it to calculate the sample size. Once the margin of error is defined, you can substitute it into the formula to find the required sample size.