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 the sample size needed in order to estimate the proportion of female students at DeVry University within a certain margin of error, we can use the formula for sample size calculation for a proportion.
The formula for sample size needed to estimate a proportion is given by:
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 (in this case, it is the Z-score for a 95% confidence level, which is approximately 1.96)
p is the estimated proportion (if we don't have any estimate, we can use 0.5 for a conservative estimate)
E is the desired margin of error (in this case, 4% or 0.04)
Plugging in the values, we have:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2
Simplifying this equation gives us:
n = 2401
Therefore, we would need to sample at least 2401 students from DeVry University in order to estimate the proportion of female students within 4% with a 95% confidence interval.