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Interval estimation is a crucial statistical method that utilizes inductive reasoning to generalize from specific data points. A statistic serves as a “best point estimate” for a corresponding parameter derived from a random data sample. To extend this estimate, we incorporate a “margin for error,” resulting in a range known as the interval estimate. The width of this interval is influenced by the level of confidence and the standard error. Key assumptions include the necessity for random sampling and a sample size of at least 30 observations to ensure validity.
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Method • Inductive Reasoning • Generalizing from a specific idea/notion/data-point • Start: a statistic is used as a “best point estimate” for a corresponding parameter, when it is computed using a random sample of data. • To generalize, we add and subtract a “margin for error” that creates a range of values for the parameter. This range is called the interval estimate • The width of the interval estimate is the product of 2 things: • The level of confidence, AND • The standard error of the statistic
Assumptions • Data sample must be randomly selected • The size of the sample ought to be as large as possible, and should contain at least 30 observations—according to Central Limit Theorem. • If a sample is either not randomly selected or not large enough, then an interval estimate may fail to yield a valid generalization about a parameter’s value.
