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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: 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. MeanMargin of Error: 𝐸=𝑧(𝛼/2) 𝜎/√𝑛 | Necessary Sample Size: n = 𝑧(𝛼/2) )2 𝜎2)/𝐸^2 |
Interval Estimateof a Population ProportionThe 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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