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Testing_for_Means 9.1-9.5

Testing_for_Means 9.1-9.5 - Hypothesis Testing for...

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Hypothesis Testing for Population Means Confidence Intervals and Hypothesis Testing for Population Means March 2, 2014 Confidence Intervals and Hypothesis Testing for Population
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Hypothesis Testing for Population Means Hypotheses Hypotheses are always statements about which of the following? A. The sample statistics B. The estimator C. The population parameters D. The sample size C. Confidence Intervals and Hypothesis Testing for Population
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Hypothesis Testing for Population Means Hypotheses Hypotheses are always statements about which of the following? A. The sample statistics B. The estimator C. The population parameters D. The sample size C. Confidence Intervals and Hypothesis Testing for Population
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Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Objectives After completing this module you should be able to find the critical values t * α / 2 or t * α compute a CI for a population mean conduct a hypothesis test for a population mean compute the p-value for a t-test Confidence Intervals and Hypothesis Testing for Population
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Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Sampling Distribution for the Means Confidence Intervals and Hypothesis Testing for Population
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Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Inference on the Mean The mean of the collection of the sample means will approximate the population mean μ The standard error of the mean SD = s n 1 Sampling distribution of the sample mean: ¯ X N ( μ , σ n ) 2 For a sample size of 1: X N μ , σ 1 Confidence Intervals and Hypothesis Testing for Population
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Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations CI for Population Mean Click here for Simulation of CI of the mean 1 Formula for a ( 1 - α ) 100 % CI for μ : ¯ X ± z α / 2 * σ ¯ X , where Lower limit = ¯ X - z * α / 2 * σ ¯ X Upper limit = ¯ X + z * α / 2 * σ ¯ X Questions: What level of confidence would accompany each of the following intervals: 1 sample mean ± 1.645(SD)? 2 sample mean ± 1.96(SD) or 2(SD)? 3 sample mean ± 2.575(SD)? Interpretation: Ex: In 95 % of all samples, the true population mean will be within 2 standard errors of the sample mean . Confidence Intervals and Hypothesis Testing for Population
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Hypothesis Testing for Population Means Hypothesis Testing for One Population Mean Comparing Two Means for Two Independent Populations Comparing Two Means for Two Dependent Populations Half-width and Sample Size Calculation Confidence Interval for μ : ¯ X ± z * α / 2 * σ n Half-width: h = z * α / 2 * σ n Sample size: n = z * α / 2 * σ h 2 Confidence Intervals and Hypothesis Testing for Population
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