A large sample of 18 units has a mean 20 and a standard deviation σ of 36. Find a 0.99% 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 - 0.01
α = 0.99
Find α spread range:
α = ½(α)
α = ½(0.99)
α = 0.495
Find z-score for α value for 0.495
zscore0.495 = 0 <--- Value can be found on Excel using =NORMSINV(0.505)
Calculate the Standard Error of the Mean:
| SEM = | σ |
| √n |
| SEM = | 36 |
| √18 |
| SEM = | 36 |
| 4.2426406871193 |
SEM = 8.4853
Calculate high end confidence interval total:
High End = X + zscoreα * s/√n
High End = 20 + 0 * 36/√18
High End = 20 + 0 * 8.4852813742386
High End = 20 + 0
0 can be derived on Excel below
Excel or Google Sheets formula:
Excel or Google Sheets formula:CONFIDENCE(0.99,36,18)High End = 20
Calculate low end confidence interval total:
Low End = X - zscoreα * s/√n
Low End = 20 - 0 * 36/√18
Low End = 20 - 0 * 8.4852813742386
Low End = 20 - 0
Low End = 20
Now we have everything, display our 0.99% confidence interval:
20 < μ < 20
You have 2 free calculationss remaining
What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 0.99%
What is the Answer?
20 < μ < 20
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.
This calculator has 5 inputs.
What 1 formula is used for the Confidence Interval for the Mean Calculator?
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
Example calculations for the Confidence Interval for the Mean Calculator
Confidence Interval for the Mean Calculator Video
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