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

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 - zscoreα/2 * s/√n < μ < X + zscoreα/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
zscore0.05 = 1.645 <--- Value can be found on Excel using =NORMSINV(0.95)

Calculate the Standard Error of the Mean:

SEM  =  σ

SEM  =  16.6

SEM  =  16.6

SEM = 0.5231

Calculate high end confidence interval total:
High End = X + zscoreα * 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 - zscoreα * 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:
10.4395 < μ < 12.1605

What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 90%

What is the Answer?
10.4395 < μ < 12.1605
How does the Confidence Interval for the Mean Calculator work?
Free Confidence Interval for the Mean Calculator - Calculates a (90% - 99%) estimation of confidence interval for the mean given a small sample size using the student-t method with (n - 1) degrees of freedom or a large sample size using the normal distribution Z-score (z value) method including Standard Error of the Mean. confidence interval of the mean
This calculator has 5 inputs.

What 1 formula is used for the Confidence Interval for the Mean Calculator?

SE = σ/√n

For more math formulas, check out our Formula Dossier

What 6 concepts are covered in the Confidence Interval for the Mean 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 for the mean
a way of estimating the true population mean
degrees of freedom
number of values in the final calculation of a statistic that are free to vary
A statistical measurement also known as the average
sample size
measures the number of individual samples measured or observations used in a survey or experiment.
standard error of the mean
measures how far the sample mean (average) of the data is likely to be from the true population mean
SE = σ/√n
Example calculations for the Confidence Interval for the Mean Calculator
Confidence Interval for the Mean Calculator Video


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