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Modern Business Statistics Interval Estimation Cheat Sheet by

Margin of Error and the Interval Estimate

A point estimator cannot be expected to provide the exact value of the population parameter.
An interval estimate can be computed by adding and subtra­cting a margin of error to the point estimate. Point Estimate +/- Margin of Error
The purpose of an interval estimate is to provide inform­ation about how close the point estimate is to the value of the parameter.
The general form of an interval estimate of a population mean is: 𝑥 ̅ + Margin of Error

Interval Estimate of a Pop. Mean:

Interval Estimate: 𝑥 ̅± 𝑡(𝛼/2) s/√𝑛
𝑥 ̅=the sample mean, 1-a=the confidence coeffi­cient, t(a/2)=the t value providing an area of a/2 in the upper tail of a t distri­bution with n-1 degrees of freedom, s=the sample standard deviation, n=the sample size
n=30 is usually an adequate sample size
 

Interval Estimate of a Pop. Mean:

Interval Estimate of Mean: 𝑥 ̅± 𝑧(𝛼/2) 𝜎/√𝑛
𝑥 ̅ is the sample mean, 1-a is the confidence coeffi­cient, z(a/2) is the z value providing an area of a/2 in the upper tail of the standard normal probab­ility distri­bution, 𝜎 is the population standard deviation, n is the sample size

Sample Size for an Int.l Estimate of a Pop. Mean

Margin of Error: 𝐸=𝑧(𝛼/2) 𝜎/√𝑛
Necessary Sample Size: n = 𝑧(𝛼/2) )2 𝜎2)/𝐸^2

Interval Estimate of a Population Proportion

The general form of an interval estimate of a population proportion is: 𝑝 ̅ + Margin of Error
Interval Estimate: 𝑝 ̅±𝑧(𝛼/2) √𝑝 ̅(1­−𝑝 ­̅)/𝑛)
Margin of Error: E = 𝑧(𝛼/2) √𝑝 ̅(1­−𝑝 ̅)/𝑛
Necessary Sample Size: 𝑛=𝑧(𝛼/2)2 𝑝∗ (1−𝑝∗ )/𝐸2
𝑝∗=.5
               

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