Confidence Interval for the Mean Calculator

Enter N	Enter X	Enter σ or s	Enter Confidence Interval %	Rounding Digits

   

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A large sample of 100 units has a mean 3000 and a standard deviation σ of 500. Find a 95% confidence interval of the mean μ

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

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
zscore_0.025 = 1.96 <--- Value can be found on Excel using =NORMSINV(0.975)

Calculate the Standard Error of the Mean:

SEM  =	σ
	√n

SEM  =	500
	√100

SEM  =	500
	10

SEM = 50

Calculate high end confidence interval total:
High End = X + zscore_α * s/√n
High End = 3000 + 1.96 * 500/√100
High End = 3000 + 1.96 * 50
High End = 3000 + 98
98 can be derived on Excel below

Excel or Google Sheets formula:

Excel or Google Sheets formula:CONFIDENCE(0.05,500,100)

High End = 3098

Calculate low end confidence interval total:
Low End = X - zscore_α * s/√n
Low End = 3000 - 1.96 * 500/√100
Low End = 3000 - 1.96 * 50
Low End = 3000 - 98
Low End = 2902

Now we have everything, display our 95% 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 μ would be 95%

Confidence Interval for the Mean Calculator Video

Tags:

• confidence interval for the mean
• confidence interval
• degrees of freedom
• mean
• sample size
• standard error of the mean

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