Confidence Interval for Mean of Finite Population for n = 120, X̄ = 65.25, s = 1.5, N = 1000 & 99% confidence
The probability of unknown parameter of population expected to lie between the confidence interval 64.9191 and 65.5809. The values 64.9191 and 65.5809 are the lower and upper limits of the confidence interval for mean of finite population estimated from sample size n = 120, mean X̄ = 65.25, standard deviation s = 1.5 population size N = 1000 & Z-score of confidence level for 99% = 2.575 to estimate the confidence interval for mean of finite population.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
