Confidence Interval for Mean of Infinite Population n = 100, X̄ = 57.25, s = 2.5 & 95% confidence
The probability of unknown population parameter expected to lie between the confidence interval 56.76 and 57.74. 56.76 and 57.74 are the lower and upper limits of the confidence interval for mean of infinite population estimated from sample size n = 100, sample mean X̄ = 57.25 sample standard deviation s = 2.5 & Z-score of confidence level for 95% = 1.960
Work with Steps for n = 100, X̄ = 57.25, s = 2.5 & 95% confidence
The complete work with step by step calculation for sample size n = 100, sample mean X̄ = 57.25 sample standard deviation s = 2.5 & Z-score of confidence level for 95% = 1.960 to estimate the confidence interval for mean of infinite population in statistical experiments.
Workout :
step 1 Address the formula input parameters and values
Sample size n = 100
Sample mean X̄ = 57.25
Sample standard deviation σ = 2.5
Z-score for 95% confidence level = 1.960
step 2 Substitute sample size, point estimate of population mean, sample standard deviation & Z-score in the below confidence interval formula
= 57.25 ± 1.9602.5√100
step 3 Simplify the above expression
= 57.25 ± 1.9602.510
= 57.25 ± 1.960 x 0.25
= 57.25 ± 0.49
57.25 + 0.49 = 57.74 or 57.25 - 0.49 = 56.76
The lower limit is 56.76 and
The upper limit is 57.74
56.76 & 57.74 are the lower and upper limits of the confidence interval for n = 100, X̄ = 57.25, s = 2.5 & Z = 1.960
