What is confidence interval of a mean or a proportion? What’s margin of error? How to obtain both?
Solution :
Confidence interval estimate of the population mean
Point estimate = sample mean =
Population standard deviation =
Sample size = n
At 99% confidence level the z is ,
= 1 - 99% = 1 - 0.99 = 0.01
/ 2 = 0.01 / 2 = 0.005
Z/2 = Z0.005 = 2.576
Margin of error = E = Z/2* ( /n)
At 99% confidence interval estimate of the population mean is,
- E < < + E
Confidence interval for population proportion p
Point estimate = sample proportion = = x / n
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z/2 = Z 0.05 = 1.645
Margin of error = E = Z / 2 * (( * (1 - )) / n)
A 95% confidence interval for population proportion p is ,
- E < p < + E
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