Inferential Stats: Confidence Intervals & Hypothesis Testing for Two Population Means, Study notes of Data Analysis & Statistical Methods

Download Inferential Stats: Confidence Intervals & Hypothesis Testing for Two Population Means and more Study notes Data Analysis & Statistical Methods in PDF only on Docsity! 10/18/2007 1 Chapter 9 Inferences Based on Two Samples: Confidence Intervals and Tests of Hypothesis Identifying the Target Parameter Parameter Key Words or Phrases Mean difference; difference in averages1 2 μ μ− 2 Difference between proportions, percentage, fractions or rates 1 2p p− Comparing Two Population Means: Independent Sampling Confidence Intervals and hypothesis testing can be done for both large and small samples 3 Large sample cases use z-statistic, small sample cases use t-statistic When comparing two population means, we test the difference between the means Comparing Two Population Means: Independent Sampling Large Sample Confidence Interval for μ1 - μ2 ( ) ( ) ( ) 2 2 2 1 221221 21 nn zxxzxx xx σσσ αα +±−=±− − 4 assuming independent sampling, which provides the following substitution 21 ( ) 2 2 2 1 2 1 2 2 2 1 2 1 21 n s n s nnxx +≈+=− σσσ Comparing Two Population Means: Independent Sampling Properties of the Sampling Distribution of (x1-x2) •Mean of Sampling distribution (x1-x2) is (μ1-μ2) •Assuming two samples are independent, the standard deviation of the sampling distribution is 5 •The sampling distribution of (x1-x2) is approximately normal for large samples by the CLT ( ) 2 2 2 1 2 1 21 nnxx σσσ +=− Comparing Two Population Means: Independent Sampling Large Sample Test of Hypothesis for μ1 - μ2 One-Tailed Test Two-Tailed Test H0:(μ1-μ2) = D0 H0:(μ1-μ2) = D0 Ha:(μ1-μ2) <D0 Ha:(μ1-μ2) ≠ D0 6 [or Ha:(μ1-μ2) >D0] Where D0 = hypothesized difference between the means Test Statistic ( ) ( )21 021 xx Dxx z − −− = σ where ( ) 2 2 2 1 2 1 21 nnxx σσ σ += − Rejection region: z < -zα Rejection region: ⏐z⏐ > zα/2 [or z > zα when Ha:(μ1-μ2) >D0]