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10.2 Means sd Unknown

# 10.2 Means sd Unknown - Outcome 10.2Be able to use the t...

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Hypothesis Tests Statistical Inference About Means and Proportions with Two Populations BUQU 1230 Esther Tiessen Outcome 10.2—Be able to use the t distribution to conduct statistical inferences about the difference between two population means when σ1 and σ2 are unknown.

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Hypothesis Tests Two Populations Statistical inference about the difference between two population: ü 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 t -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 use s1 and s2 to estimate population standard deviations use t -distribution for making inferences expected value is Statistical Inference about the Difference between Two Population Means (σ1 and σ2 unknown) d = x 1 - 2 E d = x 1 - x 2 ( 29 1 2 s d = s 1 2 n 1 + s 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 use s1 and s2 to estimate population standard deviations use t -distribution for making inferences expected value is Statistical Inference about the Difference between Two Population Means (σ1 and σ2 unknown) d = x 1 - 2 E d = x 1 - x 2 ( 29 1 2 s d = s 1 2 n 1 + s 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 unknown) d = x 1 - 2
Hypothesis Tests Statistical Inference about the Difference between Two Population Means (σ1 and σ2 unknown) Population Mean parameter μ point estimator standard error margin of error interval estimate degrees of freedom x σ x = s n t α 2 s n ± t 2 s n n - 1 Recall from chapter 8

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Hypothesis Tests Statistical Inference about the Difference between Two Population Means (σ1 and σ2 unknown) Population Mean Difference Between 2 Population Means parameter μ D = μ 1 – μ 2 point estimator standard error margin of error interval estimate degrees of freedom x d = x 1 - 2 σ = s n s d = s 1 2 n 1 + s 2 2 n 2 t α 2 s n t 2 s 1 2 n 1 + s 2 2 n 2 ± t 2 s n ± t 2 s 1 2 n 1 + s 2 2 n 2 n - 1 df = s 1 2 n 1 + s 2 2 n 2 ( 29 2 1 n 1 - 1 s 1 2 n 1 (29 2 + 1 n 2 - 1 s 2 2 n 2 2
Hypothesis Tests Statistical Inference about the Difference between Two Population Means (σ1 and σ2 unknown) Population Mean Difference Between 2 Population Means parameter μ D = μ 1 – μ 2 point estimator standard error margin of error interval estimate

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10.2 Means sd Unknown - Outcome 10.2Be able to use the t...

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