Formulas for Chapter 7 & 8-STA 2122.pdf - Formulas for Chapter 7 8 STA 2023 Fall 19 prof Balius Topic 7.1 Estimating a Population Proportion • •

Formulas for Chapter 7 & 8-STA 2122.pdf - Formulas for...

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Formulas for Chapter 7 & 8 STA 2023 Fall 19 prof Balius Topic 7.1 Estimating a Population Proportion: A point estimate is the value of a statistic that estimates the value of a parameter. A confidence interval for an unknown parameter consists of an interval of numbers based on a point estimate. The level of confidence represents the expected proportion of intervals that will contain the parameter if a large number of different samples is obtained. The level of confidence is denoted (1 α ) · 100%. Confidence interval estimates for the population proportion are of the form
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Point estimate ± margin of error. The margin of error of a confidence interval estimate of a parameter is a measure of how accurate the point estimate is. The margin of error depends on three factors: 1)Level of confidence: As the level of confidence increases, the margin of error also increases. 2)Sample size: As the size of the random sample increases, the margin of error decreases. 3)Standard deviation of the population: The more spread there is in the population, the wider our interval will be for a given level of confidence. Constructing a (1 α ) · 100% Confidence Interval for a Population Proportion Interpretation of a Confidence Interval A (1 α ) · 100% confidence interval indicates that (1 α ) · 100% of all simple random samples of size n from the population whose parameter is unknown will result in an interval that contains the parameter.
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