Interpretation of Confidence Intervals

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Interpretation of Confidence Intervals Jim Bohan Manheim Township School District Lancaster, Pennsylvania jim_bohan@mtwp.k12.pa.us

Two Tasks in Inference Confidence Intervals: Estimate the value a parameter from a sample. Tests of Significance Test a claimed value of a parameter using the results of a sample.

The Concept Behind the Formulas ALL Confidence Intervals are computed by: The critical value is chosen from the sampling distribution to achieve the specified confidence level.

Calculation Formulas The formulas for the computation of confidence intervals are quite straightforward and mechanical. The meaning of the interval is less mechanical! Proportions Means

Acceptable Interpretation 95% Confidence Level When many samples of size n are taken from the population, 95% of those samples will have confidence intervals that “capture” or “cover” the population parameter. The interpretation is about the intervals - NOT about the probability that YOUR interval covers the population parameter!

Acceptable Interpretation 95% Confidence Interval I am 95% confident that my interval covers (or contains) the population parameter.