Cheatography

# Modern Business Statistics Interval Estimation Cheat Sheet by allyrae97

### 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: π₯Β Μ + Margin of Error

### Interval Estimate of a Pop. Mean:

 Interval Estimate: π₯Β ΜΒ± π‘(πΌ/2) s/βπ π₯Β Μ=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: π₯Β ΜΒ± π§(πΌ/2) π/βπ π₯Β Μ 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, π is the population standard deviation, n is the sample size

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

 Margin of Error: πΈ=π§(πΌ/2) π/βπ Necessary Sample Size: n = π§(πΌ/2) )2 π2)/πΈ^2

### Interval Estimate of a Population Proportion

 The general form of an interval estimate of a population proportion is: πΒ Μ + Margin of Error Interval Estimate: πΒ ΜΒ±π§(πΌ/2) βπΒ Μ(1­βπΒ ­Μ)/π) Margin of Error: E = π§(πΌ/2) βπΒ Μ(1­βπΒ Μ)/π Necessary Sample Size: π=π§(πΌ/2)2 πβ (1βπβ )/πΈ2 πβ=.5