Construct a 99% confidence interval for the proportion value p from a population of 300 and a sample size of 120

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

Find z-score for α value for 0.005 zscore_{0.005} = 2.576 <--- Value can be found on Excel using =NORMSINV(0.995)

Calculate Margin of Error:

MOE = σ_{p} x z-score MOE = 0.028284271247462 x 2.576 MOE = 0.072860282733462

Calculate high end confidence interval total:

High End = p^+ zscore_{α} x σ_{p} High End = 0.4 + 2.576 * 0.028284271247462 High End = 0.4 + 0.072860282733462 High End = 0.4729

Calculate low end confidence interval total:

Low End = p^ - zscore_{α} x σ_{p} Low End = 0.4 - 2.576 * 0.028284271247462 Low End = 0.4 - 0.072860282733462 Low End = 0.3271

Now we have everything, display our 99% confidence interval:

0.3271 < p < 0.4729

What this means is if we repeated experiments, the proportion of such intervals that contain p would be 99%

What is the Answer?

0.3271 < p < 0.4729

How does the Confidence Interval of a Proportion Calculator work?

Free Confidence Interval of a Proportion Calculator - Given N, n, and a confidence percentage, this will calculate the estimation of confidence interval for the population proportion π including the margin of error. confidence interval of the population proportion This calculator has 3 inputs.

What 3 formulas are used for the Confidence Interval of a Proportion Calculator?