95 Confidence Interval Calculator

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95% Confidence level is usually considered as the desired level of confidence in Statistics for a given sample

mean. If we consider 100 different samples and evaluate 95% confidence interval for each sample, then 95%

confidence interval means nearly 95 out of 100 confidence interval contains the true population mean. 95

Confidence interval calculator is the online tool which can evaluate this interval value.



Example 1: Given sample size in a given population is 12. If the standard deviation is 22 and the

sample mean is 30, find the 95% confidence interval for the given mean number.



In order to find the 95% confidence interval (μ), we can use the formula:

x - tα/2(σ/√n) < μ < x + tα/2(σ/√n)

where x = Sample mean = 30

σ = standard deviation = 22

n = sample size = 12

tα/2 = 2.2010(from the t – alpha values table)

30 – (2.2010 * 22/√12) < μ <30 – (2.2010 * 22/√12)

16.02< μ <43.98



Example 2: Given sample size in a given population is 5. If the standard deviation is 7 and the

sample mean is 16, find the 95% confidence interval for the given mean number.



In order to find the 95% confidence interval (μ), we can use the formula:

x - tα/2(σ/√n) < μ < x + tα/2(σ/√n)

where x = Sample mean = 16

σ = standard deviation = 7

n = sample size = 5

tα/2 = 2.7764 (from the t – alpha values table)

16 – (2.7764 * 7/√5) < μ <16 – (2.7764 * 7/√5)

7.308<μ <24.69

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