Confidence Interval for the Mean Calculator

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

   

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Since you were not sure what test to use, we evaluate our sample size of n = 1007
Since our sample size was greater than 30, we use the Large Sample Normal Distribution Confidence Interval Test

A large sample of 1007 units has a mean 11.3 and a standard deviation σ of 16.6. Find a 90% 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 - 0.9
α = 0.1

Find α spread range:
α = ½(α)
α = ½(0.1)
α = 0.05

Find z-score for α value for 0.05
zscore_0.05 = 1.645 <--- Value can be found on Excel using =NORMSINV(0.95)

Calculate the Standard Error of the Mean:

SEM  =	σ
	√n

SEM  =	16.6
	√1007

SEM  =	16.6
	31.733263305245

SEM = 0.5231

Calculate high end confidence interval total:
High End = X + zscore_α * s/√n
High End = 11.3 + 1.645 * 16.6/√1007
High End = 11.3 + 1.645 * 0.5231103980805
High End = 11.3 + 0.86051660484242
0.86051660484242 can be derived on Excel below

Excel or Google Sheets formula:

Excel or Google Sheets formula:CONFIDENCE(0.1,16.6,1007)

High End = 12.1605

Calculate low end confidence interval total:
Low End = X - zscore_α * s/√n
Low End = 11.3 - 1.645 * 16.6/√1007
Low End = 11.3 - 1.645 * 0.5231103980805
Low End = 11.3 - 0.86051660484242
Low End = 10.4395

Now we have everything, display our 90% 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 90%

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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