Question 1202947
p = 325 / 500 = .65
q = 1 - p = 1 - .65 = .35
95% two tailed confidence interval requires a critical z-score of plus or minus 1.95966.
z-score formula is z = (x-m)/s
z = z-score
x is the population mean
m is the sample mean
(x-m) is the margin of error.
s is the standard error.
in a proportion type study, s is equal to sqrt(p * q / n) sqrt(.65 * .35 / 500) = .02133.
when the critical z-score is - 1.95996, the formula becomes -1.95996 = (.65 - m) / .02133.
solve for (.65 - m) to get (.65 - m) = -1.95996 * .02133 = -.0418059.
solve for m to get m = .65 + .0418059 = .6918059.
when the critical z-score is 1.95996, the formula becomes 1.95996 = (.65 - m) / .02133.
solve for (.65 - m) to get (.65 - m) = 1.95996 * .02133 = .0418059.
solve for m to get m = .65 - .0418059 = .6081941
your 95% confidence interval is from .6081941 to .6918059
your margin of error is .0418059.


here's what it looks like on a graph.


the first two graphs use z-scores
the second two graphs use raw scores
the first graph of each pair is looking for the confidence interval (area) based on the scores.
the second graph of each pair is looking for the scores based on the confidence interval.


when looking for z-scores, the mean is 0 and the standard deviation is 1.
when looking for raw scores, the mean is .65 and the standard deviation is .02133.
what is shown as the standard devition is really the standard error.


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