A large sample of 12 units has a mean 24 and a standard deviation σ of 30. Find a 0.95% 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
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 =
30
√12
SEM =
30
3.4641016151378
SEM = 8.6603
Calculate high end confidence interval total: High End = X + zscoreα * s/√n High End = 24 + 0 * 30/√12 High End = 24 + 0 * 8.6602540378444 High End = 24 + 0 0 can be derived on Excel below
Excel or Google Sheets formula:
Excel or Google Sheets formula:CONFIDENCE(0.99,30,12)
High End = 24
Calculate low end confidence interval total: Low End = X - zscoreα * s/√n Low End = 24 - 0 * 30/√12 Low End = 24 - 0 * 8.6602540378444 Low End = 24 - 0 Low End = 24
Now we have everything, display our 0.95% confidence interval:
24 < μ < 24
You have 2 free calculationss remaining
What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 0.95%
What is the Answer?
24 < μ < 24
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?