99% Proportion Confidence Interval 120/300

99% Proportion Confidence Interval 120/300 Image to Crop

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

σ_p =	√p^(1 - p^)
	√N

σ_p =	√0.4(1 - 0.4)
	√300

σ_p =	√0.4(0.6)
	√300

σ_p =	√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:

0.3271 < p < 0.4729

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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?

p^ = n/N
α = 1 - Confidence%
p^ - zscore_α * σ_p/√ p < p < p^ + zscore_α * σ_p/√p

For more math formulas, check out our Formula Dossier

What 5 concepts are covered in the Confidence Interval of a Proportion Calculator?

confidence interval: a range of values so defined that there is a specified probability that the value of a parameter lies within it.
confidence interval of a proportion: the probability that a population parameter will fall between a set of values for a certain proportion of times.
margin of error: a statistic expressing the amount of random sampling error in the results of a survey.
σ_p + z-score
population: all the inhabitants of a particular town, area, or country.
proportion: n equation in which two ratios are set equal to each other
a/b = c/d