ConfidenceInterval

# ConfidenceInterval - Student Lecture Notes 1 Introduction...

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Student Lecture Notes 1 ConfidenceIntervals 1 1 Introduction to Inference Confidence Interval (CI) ± Based on a Single Sample ± Confidence Level (CL) ± Level of Significance ± Significance Tests ± Mean ± Proportion ± Normal (z) and ± Student’s t distributions Hypothesis 2 Using Sample Statistic, Estimate Population Parameter ± Point estimate, single value ± Population Mean ± Population Proportion ± Interval estimate, range of values ± Population Mean ± Population Proportion ± Sample size to achieve desired accuracy

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Student Lecture Notes 2 ConfidenceIntervals 2 Hypothesis 3 Estimation Process for Population Parameter ± Population ± Population has unknown mean (proportion) ± Draw a SRS (Simple Random Sample) ± Obtain Sample Statistics ± sample mean (proportion) ± Use Confidence Level (probability of having true parameter value inside CI) to estimate interval for unknown population parameter (mean or proportion) using sample statistic: ± Estimate +/- Margin of Error Hypothesis 4 Unknown Population Parameters Are Estimated Estimate population Estimate population parameter. .. parameter. .. with sample with sample statistic statistic Mean Mean μ x Proportion Proportion p p ^ Variance Variance σ 2 s 2 Differences Differences μ 1 - μ 2 x 1 - x 2
Student Lecture Notes 3 ConfidenceIntervals 3 Hypothesis 5 Point Estimation Based on 1 Sample ± Provides single value estimate of population parameter (sample mean or proportion for population value) ± No information about how close value is to unknown population parameter ± Example: Sample mean x = 6 is point estimate of unknown population mean Hypothesis 6 Interval Estimation Based on 1 Sample ± Interval estimate provides range of values ± Information about range of values for unknown population parameter ± Based on probability of being in range ± Knowing exact closeness would require knowing unknown population parameter ± Example: unknown population mean lies between 50 & 70 with 95% confidence ± 95% of sample means will be in range ± 95% of time population parameter inside CI

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Student Lecture Notes 4 ConfidenceIntervals 4 Hypothesis 7 Confidence Interval Basics ± CI at given Confidence Level Hypothesis 8 Confidence interval interval Key Elements of Interval Estimation Sample statistic (point estimate) (point estimate) Confidence Confidence limit (lower): limit (lower): Statistic Statistic -Error Error Confidence Confidence limit (upper): limit (upper): Statistic+Error Statistic+Error A probability probability that the true population that the true population parameter falls somewhere within the parameter falls somewhere within the interval Statistic Estimate+/ -Margin of Error. Margin of Error.
Student Lecture Notes 5 ConfidenceIntervals 5 Hypothesis 9 Confidence Interval at a Confidence Level ± Confidence Level Hypothesis 10 CI for Large Sample Size and/or Known Population STD ± CI for Population mean based on sample statistic

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Student Lecture Notes 6 ConfidenceIntervals 6 Hypothesis 11 Confidence Interval and Sample Size ±
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## This note was uploaded on 09/25/2009 for the course IDS 371 taught by Professor Staff during the Spring '08 term at Ill. Chicago.

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ConfidenceInterval - Student Lecture Notes 1 Introduction...

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