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Margin of Error and the Interval EstimateA 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‘(πΌ/2) s/βπ | 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§(πΌ/2) π/βπ | 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. MeanMargin of Error: πΈ=π§(πΌ/2) π/βπ | Necessary Sample Size: n = π§(πΌ/2) )2 π2)/πΈ^2 |
Interval Estimateof a Population ProportionThe general form of an interval estimate of a population proportion is: πΒ Μ
+ Margin of Error | Interval Estimate: πΒ Μ
Β±π§(πΌ/2) βπΒ Μ
(1βπΒ Μ
)/π) | Margin of Error: E = π§(πΌ/2) βπΒ Μ
(1βπΒ Μ
)/π | Necessary Sample Size: π=π§(πΌ/2)2 πβ (1βπβ )/πΈ2 | πβ=.5 |
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