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

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 - 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 - 0.99
α = 0.01

α = ½(α)
α = ½(0.01)
α = 0.005

Find z-score for α value for 0.005
zscore0.005 = 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 12.2066

SEM = 0.8192

Calculate high end confidence interval total:
High End = X + zscoreα * 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:

High End = 63.1103

Calculate low end confidence interval total:
Low End = X - zscoreα * 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:
58.8897 < μ < 63.1103

What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 99%

58.8897 < μ < 63.1103
##### 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
mean
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