How many students must we sample if we want to be within 4% of the true proportion of female students at DeVry University when using a 95% confidence interval?
To determine how many students you need to sample in order to be within 4% of the true proportion of female students at DeVry University with a 95% confidence interval, you would need to use the formula for sample size calculation for proportions.
The formula to calculate the sample size for proportions is given by:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n represents the sample size
- Z is the z-score corresponding to the desired level of confidence (in this case, 95% confidence level corresponds to a z-score of approximately 1.96)
- p is the estimated proportion of the population (if you don't have an estimation, you can use 0.5 as a conservative estimate as it provides the maximum sample size required)
- E is the maximum margin of error or maximum acceptable difference from the true proportion
In this case, you want to be within 4% of the true proportion, so E = 0.04.
Using the formula, the sample size calculation becomes:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2
Simplifying:
n = (3.8416 * 0.25) / 0.0016
n = 0.9604 / 0.0016
n = 600.25
Finally, you round up the sample size to the nearest whole number, giving you a required sample size of approximately 601 students.