A large sample of 144 units has a mean 100 and a standard deviation σ of 70. Find a 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 0.025 zscore0.025 = 1.96 <--- Value can be found on Excel using =NORMSINV(0.975)
Calculate the Standard Error of the Mean:
SEM =
σ
√n
SEM =
70
√144
SEM =
70
12
SEM = 5.8333
Calculate high end confidence interval total: High End = X + zscoreα * s/√n High End = 100 + 1.96 * 70/√144 High End = 100 + 1.96 * 5.8333333333333 High End = 100 + 11.433333333333 11.433333333333 can be derived on Excel below
Excel or Google Sheets formula:
Excel or Google Sheets formula:CONFIDENCE(0.05,70,144)
High End = 111.4333
Calculate low end confidence interval total: Low End = X - zscoreα * s/√n Low End = 100 - 1.96 * 70/√144 Low End = 100 - 1.96 * 5.8333333333333 Low End = 100 - 11.433333333333 Low End = 88.5667
Now we have everything, display our 95% confidence interval:
88.5667 < μ < 111.4333
You have 2 free calculationss remaining
What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 95%
What is the Answer?
88.5667 < μ < 111.4333
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?