confidence interval

#1
Can anyone help with the formula for finding the confidence interval for questions such as: when surveying 500 people, 200 responde yes so the proportion of yes responses from the whole population is estimated at 0.4 since .04 has been given why would we need a confidence interval?
 
#2
Cause it is an estimate of the unobserved mean in the whole population and not the unobserved true mean of the whole population.

Key here is you know exactly the sample mean. However, the sample mean is not going to be the mean of the whole population. So you need a statement about how close you expect your sample mean to be to the unobserved whole population mean. Thats what the standard error is about.
 
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#3
What you have is a sample mean. The sample mean is an estimate of the real world (population mean). Since it is an estimate it comes with some level of uncertainty.

See confidence interval concept here:
http://www.global-i-tech.co.uk/204.html

You can find a step by step numerical example here:
http://www.global-i-tech.co.uk/205.html

Hope this helps.

bbkaran

Can anyone help with the formula for finding the confidence interval for questions such as: when surveying 500 people, 200 responde yes so the proportion of yes responses from the whole population is estimated at 0.4 since .04 has been given why would we need a confidence interval?