99% Proportion Confidence Interval 120/300

Enter N	Enter n	Enter Confidence Interval %

 

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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

Calculate p^:

p^  =	n
	N

p^  =	120
	300

p^ = 0.4

Calculate σ_p

σp  =	√p^(1 - p^)
	√N

σp  =	√0.4(1 - 0.4)
	√300

σp  =	√0.4(0.6)
	√300

σp  =	√0.24
	√300

σ_p√0.0008
σ_p = 0.028284271247462

Calculate α:
α = 1 - Confidence%
α = 1 - 0.99
α = 0.01

Find α spread range:
α = ½(α)
α = ½(0.01)
α = 0.005

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:

You have 2 free calculationss remaining

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

Confidence Interval of a Proportion Calculator Video

Tags:

• confidence interval of a proportion
• confidence interval
• margin of error
• population
• proportion

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