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A point estimator cannot be expected to provide the exact value of the population parameter.
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An interval estimate can be computed by adding and subtracting a margin of error to the point estimate. Point Estimate +/- Margin of Error
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The purpose of an interval estimate is to provide information about how close the point estimate is to the value of the parameter.
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The general form of an interval estimate of a population mean is: π₯Β Μ
+ Margin of Error
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Interval Estimate: π₯Β Μ
Β± π‘(πΌ/2) s/βπ
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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
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n=30 is usually an adequate sample size
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Interval Estimate of Mean: π₯Β Μ
Β± π§(πΌ/2) π/βπ
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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
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Margin of Error: πΈ=π§(πΌ/2) π/βπ
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Necessary Sample Size: n = π§(πΌ/2) )2 π2)/πΈ^2
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The general form of an interval estimate of a population proportion is: πΒ Μ
+ Margin of Error
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Interval Estimate: πΒ Μ
Β±π§(πΌ/2) βπΒ Μ
(1βπΒ Μ
)/π)
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Margin of Error: E = π§(πΌ/2) βπΒ Μ
(1βπΒ Μ
)/π
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Necessary Sample Size: π=π§(πΌ/2)2 πβ (1βπβ )/πΈ2
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πβ=.5
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