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 μConfidence 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
Find α spread range:
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 |
| 12.206555615734 |
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:
Excel or Google Sheets formula:CONFIDENCE(0.01,10,149)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
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What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 99%
What is the Answer?
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?
What 6 concepts are covered in the Confidence Interval for the Mean Calculator?
confidence intervala 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 meandegrees of freedomnumber of values in the final calculation of a statistic that are free to varymeanA statistical measurement also known as the averagesample sizemeasures the number of individual samples measured or observations used in a survey or experiment.standard error of the meanmeasures how far the sample mean (average) of the data is likely to be from the true population meanSE = σ/√n
Example calculations for the Confidence Interval for the Mean Calculator
Confidence Interval for the Mean Calculator Video
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