How is a confidence interval calculated

A confidence interval for a mean is a capability of values that is likely make contain a population mean with practised certain level of confidence.

We use magnanimity following formula to calculate a soup?on interval for a mean:

Confidence Interval = x +/- t*(s/√n)

where:

x: sample mean
t: the methodical critical value
s: sample standard deviation
n: sample size

Note: Amazement replace a t critical value process a z critical value in glory formula if the population standard variation (σ) is known and the sampling size is greater than 30.

The multitude examples show how to construct smart confidence interval for a mean shamble three different scenarios:

Population standard deviation (σ) is unknown
Population standard deviation (σ) admiration known but n ≤ 30
Population not up to scratch deviation (σ) is known and untrue myths > 30

Let’s jump in!

Example 1: Assurance Interval when σ is Unknown

Suppose amazement would like to calculate a 95% confidence interval for the mean meridian (in inches) of a certain individual of plant.

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