Confidence Interval for Mean of Finite Population for n = 120, X̄ = 65.25, s = 1.5, N = 1000 & 99% confidence

Work with Steps for n = 120, X̄ = 65.25, s = 1.5, N = 1000 & 99% confidence
The complete work with step by step calculation for sample size n = 120, sample mean X̄ = 65.25, standard deviation s = 1.5, population size N = 1000 & Z-score for confidence level 99% = 2.575 to estimate the confidence interval for mean of finite population in statistical experiments.
Workout :
step 1 Address the formula input parameters and values
Sample size n = 120
Sample mean X̄ = 65.25
Sample standard deviation σ = 1.5
Population sample size N = 1000
Z-score for 99% confidence level = 2.575
Population size N = 1000
step 2 Substitute sample size, point estimate of population mean, sample standard deviation & Z-score in the below confidence interval formula
= 65.25 ± 2.5751.5√120√(1000 - 120)/(1000 - 1)
step 3 Simplify the above expression
= 65.25 ± 2.5751.5√120√880/999
= 65.25 ± 2.5751.510.9545√0.8809
= 65.25 ± 2.575 x 0.1369 x 0.9386
= 65.25 ± 0.3309
65.25 + 0.3309 = 65.5809 or 65.25 - 0.3309 = 64.9191
The lower limit is 64.9191 and
The upper limit is 65.5809
64.9191 & 65.5809 are the lower and upper limits of the confidence interval for n = 120, X̄ = 65.25, s = 1.5, N = 1000 & Z = 2.575
