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Understanding Sampling Distribution and Estimation for Population Means

This work by Dr. Saba M. Alwan explores the concepts of sampling distributions, point estimation, and interval estimation for population means (µ). It addresses scenarios with known and unknown standard deviations (σ), both for large samples (n ≥ 30) and small samples (n < 30). The principles of hypothesis testing related to means and differences of means (µ1 - µ2) are also covered, highlighting the importance of normality and sample size in statistical analysis. An essential read for understanding estimation techniques in statistics.

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Understanding Sampling Distribution and Estimation for Population Means

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  1. Dr. Saba M. Alwan Population with mean µ Sampling Distribution of The mean , Not- normal Normal σ is known σ is Unknown σ is Unknown σ is known n ≥ 30 n < 30 Not in study

  2. Estimation Dr. Saba M. Alwan Population with mean µ A good Point estimate for µ is Interval Estimation or (C.I) for the mean µ Not- normal Normal σ is known σ is Unknown σ is Unknown σ is known n ≥ 30 n < 30 Not in study

  3. Testing Dr. Saba M. Alwan Sample size Test statistic in testing hypothesis for the mean μ : n<30 n≥30 σ is known σ is Unknown σ is Unknown σ is known normal or not normal normal not normal Not in study

  4. Estimation Dr. Saba M. Alwan A good point estimate for (μ1 - μ2) is Sample sizes Interval Estimation or (C.I) for the mean (μ1 - μ2) at α: n1 and n2 <30 (Small) n1, n2 ≥30 (Large) normal or not normal normal not normal σ1 , σ2 Unknown But Equal σ1 and σ2Unknown σ1 , σ2 known σ1 , σ2 known Not in study

  5. Testing Dr. Saba M. Alwan Sample sizes Test statistic in testing hypothesis for the difference d = (μ1 - μ2) : n1, n2 ≥30 (Large) n1 and n2 <30 (Small) normal or not normal normal not normal σ1 , σ2 Unknown But Equal σ1 and σ2Unknown σ1 , σ2 known σ1 , σ2 known Not in study where d = (μ1 - μ2)

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