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2.2 Interval Estimation - sigma unknown [Key Concepts]

# 2.2 Interval Estimation - sigma unknown [Key Concepts] - Dr...

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© 2009 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management 2 Confidence Interval Estimation of Means 2.2 σ Unknown Dr. Harvey A. Singer School of Management George Mason University

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© 2009 by Harvey A. Singer 2 Confidence Interval for μ : σ Unknown Assumptions: Population standard deviation σ is unknown. But σ is estimated from the value of the sample standard deviation s . Population must be normally distributed. Still true that where E is the margin of error. But E is different because σ is unknown. Use s as the point estimate for σ . E x E - x + μ
© 2009 by Harvey A. Singer 3 Problems with σ Unknown Error from the accident of sampling (as before). Error using s as a first and best guess for σ . Error because of the finite size of the sample. Because of the finite sample size, there is the very strong likelihood that the sample is not representative of the population. As before, but magnified because s is used to estimate σ . A very big issue if the sample size is small ( n < 30).

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© 2009 by Harvey A. Singer 4 The Problems As a result, cannot use the normal distribution as a model for the sampling distribution of the
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2.2 Interval Estimation - sigma unknown [Key Concepts] - Dr...

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