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 149 units has a mean 61 and a standard deviation σ of 10. Find a 99% 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 - 0.99
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 the Standard Error of the Mean:

SEM  =	σ
	√n

SEM  =	10
	√149

SEM  =	10
	12.206555615734

SEM = 0.8192

Calculate high end confidence interval total:
High End = X + zscore_α * s/√n
High End = 61 + 2.576 * 10/√149
High End = 61 + 2.576 * 0.81923192051904
High End = 61 + 2.110341427257
2.110341427257 can be derived on Excel below

Excel or Google Sheets formula:

Excel or Google Sheets formula:CONFIDENCE(0.01,10,149)

High End = 63.1103

Calculate low end confidence interval total:
Low End = X - zscore_α * s/√n
Low End = 61 - 2.576 * 10/√149
Low End = 61 - 2.576 * 0.81923192051904
Low End = 61 - 2.110341427257
Low End = 58.8897

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 μ would be 99%

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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