Stat 344 Lecture 18 (17), Confidence Intervals for mean and proportion

# Stat 344 Lecture 18 (17), Confidence Intervals for mean and proportion

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Concepts of Point Estimation Lecture 18 (former 17) Topics Basic properties of a confidence interval Large-sample confidence intervals Population mean for measurement data Population proportion for categorical data Bootstrap confidence intervals – ignore Confidence bounds Lecture 17 Reference: Devore Sec 7.1 Basic properties of confidence intervals Sec 7.2 Large-sample confidence intervals for the . 1 Stat 344 Lecture 17

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Point Estimates Point estimates of a population parameter are a single number (statistic) calculated from a sample. For the population mean => x-bar For the population proportion => p-hat A confidence interval is a range that has a given probability of including the true population parameter. A narrow interval has greater precision . The estimate of the Brand 1 parameter is more precise than that of 2. 2 Stat 344 Lecture 17
Confidence Interval of the Mean We desire to estimate the population mean (μ) Initial assumptions (to be removed later) : The population distribution is normal. The value of the population standard deviation is known. X-bar is the point estimate of μ The interval of the estimate for μ is X-bar ± the margin of error : 3 Stat 344 Lecture 17

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Interpretation About 95% of the intervals will include the population mean (per prior slide). X-bar is the random variable & center of the interval. The interval is X-bar ± margin of error. 10 of these 11
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Stat 344 Lecture 18 (17), Confidence Intervals for mean and proportion

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