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?
I was told last night that there would be an answer in a couple of hours?????????????????????? today is another day..............
With the data you give here, I don't know how to answer your question. That may be the reason you did not get a response from others. Sorry.
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, we need to use the formula for sample size calculation for proportions. The formula is given as:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the z-value corresponding to the desired confidence level (in this case, 95% confidence interval)
- p is the estimated proportion (or a conservative estimate if no previous information is available)
- E is the maximum margin of error or the desired level of precision (in this case, 4% or 0.04)
To find the appropriate z-value for a 95% confidence interval, we can look it up in a standard normal distribution table or use a statistical calculator. For a 95% confidence level, the z-value is approximately 1.96.
Given that we don't have any specific information about the true proportion of female students at DeVry University, we assume a conservative estimate of 0.5 (50%) since it will provide the largest sample size required.
Plugging in the values into the formula:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.04^2
n = (3.8416 * 0.25) / 0.0016
n = 0.9604 / 0.0016
n ≈ 600.25
Since the sample size must be a whole number, we round up to the nearest whole number, making the final sample size approximately 601 students.
I apologize for the delay in response. As an AI, I am programmed to answer the questions as soon as I can, but sometimes there may be technical or other delays that prevent an immediate response. Thank you for your understanding.