10.1 Mean sd Known

# 10.1 Mean sd Known - Outcome 10.1 Using the sampling...

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Hypothesis Tests Statistical Inference About Means and Proportions with Two Populations BUQU 1230 Esther Tiessen Outcome 10.1— Using the sampling distribution of , be able to develop interval estimates and conduct hypothesis tests about the difference between two population means when σ1 and σ2 are known. x 1 - x 2

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Hypothesis Tests Two Populations Statistical inference about the difference between two population: means (σ1 and σ2 known) means (σ1 and σ2 unknown) means (matched samples) proportions
Hypothesis Tests Two Populations Statistical inference about the difference between two population: means (σ1 and σ2 known) means (σ1 and σ2 unknown) means (matched samples) proportions z -Test:Two-Sample for Means

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Hypothesis Tests population parameter: D = μ 1– μ 2 to make inferences about D, take independent simple random samples from 2 populations use difference between sample means as the random variable use sampling distribution of if both populations follow normal distribution or if n1 and n2 are large enough for Central Limit Theorem to apply, then will have a normal distribution mean or expected value is standard error is Statistical Inference about the Difference between Two Population Means (σ1 and σ2 known) d = x 1 - x 2 d = x 1 - x 2 d = x 1 - x 2 E d = x 1 - x 2 ( 29 = μ 1 - μ 2 σ d = σ 1 2 n 1 + σ 2 2 n 2
Hypothesis Tests population parameter: D = μ 1– μ 2 to make inferences about D, take independent simple random samples from 2 populations use difference between sample means as the random variable use sampling distribution of if both populations follow normal distribution or if n1 and n2 are large enough for Central Limit Theorem to apply, then will have a normal distribution mean or expected value is standard error is Statistical Inference about the Difference between Two Population Means (σ1 and σ2 known) d = x 1 - x 2 d = x 1 - x 2 d = x 1 - x 2 E d = x 1 - x 2 ( 29 = μ 1 - μ 2 σ d = σ 1 2 n 1 + σ 2 2 n 2 Use for both interval estimation and hypothesis testing

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Hypothesis Tests population parameter: D = μ 1– μ 2 sampling distribution of Statistical Inference about the Difference between Two Population Means (σ1 and σ2 known) d = x 1 - x 2
Hypothesis Tests Statistical Inference about the Difference between Two Population Means (σ1 and σ2 known) Population Mean parameter μ point estimator standard error margin of error interval estimate z α 2 σ n x ± z α 2 σ n x σ x = σ n Recall from chapter 8

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Hypothesis Tests Statistical Inference about the Difference between Two Population Means (σ1 and σ2 known) Population Mean Difference Between 2 Population Means parameter μ D = μ 1 – μ 2 point estimator standard error margin of error interval estimate d = x 1 - x 2 σ d = σ 1 2 n 1 + σ 2 2 n 2 z α 2 σ n z α 2 σ 1 2 n 1 + σ 2 2 n 2 x ± z α 2 σ n d ± z α 2 σ 1 2 n 1 + σ 2 2 n 2 x σ x = σ n
Hypothesis Tests Statistical Inference about the Difference between Two Population Means (σ1 and σ2

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