Modern Business Statistics Interval Estimation Cheat Sheet by allyrae97

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

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

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

Margin of Error: 𝐸=𝑧(𝛼/2) 𝜎/√𝑛

Necessary Sample Size: n = 𝑧(𝛼/2) )^{2 𝜎}2)/𝐸^2

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)

𝑝∗=.5