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Chapter 7: Estimates Back To Chapter

7.3: Confidence Intervals

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Confidence Intervals

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7.2: Sample Proportion and Population Proportion

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7.4: Confidence Coefficient

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An unbiased point estimate is not always sufficient to accurately predict a given population parameter—for instance—population proportion or mean.

So, to get a better judgment of a population parameter, a range of values can be drawn from the sample data distribution to estimate the true value of the population parameter.

This range is called Interval Estimate, more commonly known as the Confidence Interval.

Unlike the point estimate, the confidence interval generates a range of values within two limits—one lower and one upper—generally referred to as the confidence limits.

The confidence interval for the population proportion can be represented by writing the calculated lower limit—followed by population proportion—followed by the calculated upper limit.

In this equation, Equation1 is sample proportion, Equation2 is population proportion, and E is the margin of error.

In simpler terms, it may also be expressed as Equation1 ± E.

The confidence interval indicates the uncertainty in the parameter estimate predicting the true value of the population parameter. In other words, the narrower the confidence interval, the more accurate the estimate is.

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 L_2, 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%.

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Confidence Interval Point Estimate Population Estimate Population Mean Population Proportion Confidence Limits L1 L2 Margin Of Error Confidence Level

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