What this means is if we repeated experiments, the proportion of such intervals that contain μ would be 0.99%
Answer
20 < μ < 20
↓Steps Explained:↓
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
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
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
Final Answer
20 < μ < 20Related Calculators: Confidence Interval/Hypothesis Testing for the Difference of Means | Sample Size Requirement for the Difference of Means | Sample Size Reli