determine sample size using confidence interval?

Hi all,

I've just started learning stats. Need help on some questions that I dont quite really understand just by reading the book.

How do I actually determine sample size using C.I using the below example?

Eg. a random sample size of 72 students generated a 90% confidence interval: (0.438, 0.642). Using this information, what size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

q1) Does the interval varies with different confidence lvl? How does the interval works actually?

q2) What does the true proportion mean?

q3) Is ±0.08 an error standard? How does the ±0.08 works with the interval(0.438, 0.642)?

q4) how to calculate the critical Z-value for different confidence levels?

You should have a formula in your book for calculating confidence intervals. From what I remember these are the elements you need to calculate a confidence interval:
1) a value (like the mean)
2) the standard error of the measure
3) the desired width of the CI

You can decompose the 90% CI that you were given to find some of those elements (the CI, the standard error) to get to the mean. With this new mean you can then recalculate your 95% CI with .08 standard error.

Does that make sense?

Good luck!