Confidence Interval of a Proportion Calculator

Enter N Enter n Enter Confidence Interval %

Construct a 95% confidence interval for the proportion value p from a population of 40 and a sample size of 12

Confidence Interval Formula for p is as follows:
p^ - zscoreα * σp/√p < p < p^ + zscoreα * σp/√p where:
X = sample mean, s = sample standard deviation, zscore = Normal distribution Z-score from a probability where α = (1 - Confidence Percentage)/2

Calculate p^:
p^ =n
N

p^ =12
40

p^ = 0.3

Calculate σp
σp =p^(1 - p^)
N

σp =0.3(1 - 0.3)
40

σp =0.3(0.7)
40

σp =0.21
40

σp0.00525
σp = 0.947

Calculate α:
α = 1 - Confidence%
α = 1 - 0.95
α = 0.05

Find α spread range:
α = ½(α)
α = ½(0.05)
α = 0.025

Find z-score for α value for 0.025
zscore0.025 = 1.96 <--- Value can be found on Excel using =NORMSINV(0.975)

Calculate Margin of Error:
MOE = σp x z-score
MOE = 0.947 x 1.96
MOE = 0.

Calculate high end confidence interval total:
High End = p^+ zscoreα x σp
High End = 0.3 + 1.96 * 0.947
High End = 0.3 + 0.
High End = 0.442

Calculate low end confidence interval total:
Low End = p^ - zscoreα x σp
Low End = 0.3 - 1.96 * 0.947
Low End = 0.3 - 0.
Low End = 0.158

Now we have everything, display our 95% confidence interval:
0.158 < p < 0.442

What this means is if we repeated experiments, the proportion of such intervals that contain p would be 95%