Construct a 95% confidence interval for the proportion value p from a population of 100 and a sample size of 40
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
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 = 0.048989794855664 x 1.96 MOE = 0.096019997917101
Calculate high end confidence interval total:
High End = p^+ zscoreα x σp High End = 0.4 + 1.96 * 0.048989794855664 High End = 0.4 + 0.096019997917101 High End = 0.496
Calculate low end confidence interval total:
Low End = p^ - zscoreα x σp Low End = 0.4 - 1.96 * 0.048989794855664 Low End = 0.4 - 0.096019997917101 Low End = 0.304
Now we have everything, display our 95% confidence interval:
0.304 < p < 0.496
You have 2 free calculationss remaining
What this means is if we repeated experiments, the proportion of such intervals that contain p would be 95%
What is the Answer?
0.304 < p < 0.496
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?