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Interval estimation, general form for a CI, construct CI for pi

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Colorado State University
STAT 301
Brett Hunter

19 September Interval estimation Let Δ be a fixed, but unknown parameter Let δ be the point estimate for Δ We want to know what Δ could possibly be That is, we want an interval of plausible values for Δ. δ is an approximation of Δ, but δ varies from sample to sample. However, we can use δ to create an interval of plausible values for Δ: δ ± ERROR A confidence interval for a parameter is an interval of possible values for that parameter constructed so that, with a certain degree of confidence, the values of the parameter will be captured in the interval. The confidence level is the success rate of the method used to construct the confidence interval Most common are 90%, 95%, and 99% Ideas of CIs If we had a 95% CI, then 95% of the time, the true parameter value is within the error term from the point estimate General form for a CI Point estimate = (critical value) > (standard error) δ ± ERROR SE depends on sampling distribution of the statistic (point est) Critical value depends on confidence level and sampling distribution Confidence level is important, as the more confident we are that the truth is contained in the interval, the wider out interva
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