P-Hat Confidence Interval Calculator

Publish date: 2024-06-30
P-Hat Confidence Interval Calculator MathCelebrity logo Image to Crop A large sample of 200 units has 118 cases that match a certain criteria. Find a 95% confidence interval for those who have that characteristic.

Confidence Interval Formula for those who meet the criteria is as follows:

p^ - zα/2σp^ < p < p^ + zα/2σp^ where:
z = Normal distribution Z-score from a probability where α = ½(1 - Confidence Percentage)

Calculate p^

p^  =  x
  n

p^  =  118
  200

p^ = 0.59

Calculate the failure percentage q:

q = 1 - p^
q = 1 - 0.59
q = 0.41

Calculate σp^
σp^ = √p^q/n
σp^ = √(0.59)(0.41)/200
σp^ = √0.2419/200
σp^ = √0.0012095
σp^ = 0.034777866524558

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 high end confidence interval total:

High End = p^ + zscoreασp^
High End = 0.59 + 1.96 x 0.034777866524558
High End = 0.59 + 0.068164618388134
High End = 0.6582

Calculate low end confidence interval total:

Low End = p^ - zscoreασp^
Low End = 0.59 - 1.96 x 0.034777866524558
Low End = 0.59 - 0.068164618388134
Low End = 0.5218

Now we have everything, display our 95% confidence interval:

0.5218 < p^ < 0.6582

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What is the Answer?

0.5218 < p^ < 0.6582

How does the P-Hat Confidence Interval Calculator work?

Free P-Hat Confidence Interval Calculator - Given a large sized distribution, and a success amount for a certain criteria x, and a confidence percentage, this will calculate the confidence interval for that criteria.
This calculator has 3 inputs.

What 4 formulas are used for the P-Hat Confidence Interval Calculator?

p^ = x/n
q = 1 - p^
α = 1 - Confidence%
p^ - zα/2σp^ < p < p^ + zα/2σp^

For more math formulas, check out our Formula Dossier

What 3 concepts are covered in the P-Hat Confidence Interval Calculator?

confidence intervala range of values so defined that there is a specified probability that the value of a parameter lies within it.estimatorp-hat confidence interval

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