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7.3 : Confidence Intervals

An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a sample proportion. However, unlike the point estimate which is a single value, the confidence interval contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.

A confidence interval is represented as - L1, followed by a point estimate such as sample proportion or sample mean, followed by L2. The confidence limits can be calculated as follows :

L1 = point estimate - margin of error, E

L2 = point estimate + margin of error, E

A confidence interval allows a researcher to determine the uncertainty of a point estimate in predicting the true value of a population parameter. In other words, as the confidence interval narrows, the accuracy of the point estimate in predicting the actual value of a population parameter increases.

Further, a confidence level is used to check if a confidence interval contains a population parameter. The common choices for a confidence level are 90%, 95%, and 99%.

Tags
Confidence IntervalsPoint EstimatePopulation EstimateConfidence LimitsSample ProportionSample MeanMargin Of ErrorConfidence LevelAccuracyUncertainty

From Chapter 7:

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7.3 : Confidence Intervals

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7.1 : What are Estimates?

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7.2 : Sample Proportion and Population Proportion

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7.4 : Confidence Coefficient

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7.5 : Interpretation of Confidence Intervals

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7.6 : Critical Values

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7.7 : Margin of Error

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7.8 : Sample Size Calculation

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7.9 : Estimating Population Mean with Known Standard Deviation

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7.10 : Estimating Population Mean with Unknown Standard Deviation

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7.11 : Confidence Interval for Estimating Population Mean

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