Lecture5-1

Lecture5-1 - BUAD 310 Applied Business Statistics A Quick Review Estimation of population parameters(e.g population mean and population proportion

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BUAD 310 Applied Business Statistics 2/8/10
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A Quick Review Estimation of population parameters ( e.g., population mean μ and population proportion p ) Point estimate: one number estimate such as the sample mean and the sample proportion The sampling distributions of and : approximately normal Interval estimate: confidence interval (CI) 2
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Confidence Interval CI: an interval of likely estimates that contains the true value of the population parameter which is unknown to us with a given confidence level. E.g., in the gas mileage case the mean mpg for a sample of n =49 selected cars is , and the sample std dev s =0.7992. What can we say about the true mean mpg μ based on this sample information? You are certainly 100% confident that μ > 0. Then how confident are you that µ ≥ 31? Idea: construct a (1-α)100% CI for μ of the form point estimate ± margin of error (e.g., ) 3
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Confidence Level What does the confidence level of a CI (e.g., 95%) mean? Like sample mean, CI changes from sample to sample. 95% means that for the population of all possible CI’s constructed in a given way, there is 95% probability that the true value (e.g., μ) falls in the CI. 4
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Confidence Interval vs Tolerance Interval CI bounds a population parameter (e.g., mean) with some confidence, while TI gives a range of individual measurements in a population that represents a specified proportion of the population. (Recall the empirical rule gives three tolerance intervals: 68.26% TI [ ¹ - s , ¹ + ], 95.44% TI [ ¹ -2 , ¹ +2 ], 99.73% TI [ ¹ -3 , ¹ +3 ] ) CI characterizes the behavior of the average, while TI characterizes the behavior of a range of individuals. 5
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CI for a Population Mean with Known σ 6 If sampled population has mean μ and known σ, a (1-α)100% confidence interval for μ is Note : this formula for CI will not work if the sample size is small (e.g., n<30) and the data is not normal .
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This note was uploaded on 09/05/2010 for the course BUAD 310 taught by Professor Lv during the Spring '07 term at USC.

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Lecture5-1 - BUAD 310 Applied Business Statistics A Quick Review Estimation of population parameters(e.g population mean and population proportion

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