Solved: How to calculate confidence interval ( 3 methods)

The confidence interval is a way to report the most probable value for a population’s mean μ, when the population’s standard deviation, δ is known. Confidence intervals can be quoted for any desired probability level, several samples of which are shown in the table below.

zConfidence interval (%)
0.5038.30
1.0068.26
1.5086.64
1.9695.00
2.0095.44
2.5098.76
3.0099.73
3.5099.95

There are 3 methods for calculating confidence interval and their application is dependent on the type of data provided.

Method 1: Confidence interval (CI) given population mean and variance

What is the 95% confidence interval for the amount of aspirin in a single analgesic tablet drawn from a population where μ is 250mg and δ² is 25?

solution

Xi = μ ± zδ

μ=250mg

z=1.96(the value corresponding to 95% on the  table above)

δ=5

Xi= μ ± 1.96δ

250mg ± (1.96)(5)

=250mg ± 10mg

 

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