204 110.2 - 11.2 Inferences About Two Means Independent...

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11.2 Inferences About Two Means, Independent Samples 1) Two sample Z test (comparison of two means) When testing if two population means are equal (μ 1 = μ 2 ) we use the two sample Z statistic: Z = 2 2 2 1 2 1 2 1 2 1 ) ( ) ( n n x x σ σ μ μ + - - - note: both 1 σ and 2 σ are known Note: μ 1 - μ 2 is the hypothesized difference between the means, which is assumed to be zero for the TI 2-sample Z test. This statistic has a standard normal distribution. TI: 2-SampZTest PHStat: Two sample test for the mean both 1 σ and 2 σ known Example: 1 x = 84 2 x = 91 n 1 = 16 n 2 = 16 σ 1 = 8 σ 2 = 4 test: Ho: μ 1 = μ 2 Ha: μ 1 < μ 2 α = .05 The above values yield a z = -3.1305 ( 1 x - 2 x ) And a pval = 0.000873 2) Two Sample t test For the two sample t we use the statistic: t = 2 2 2 1 2 1 2 1 2 1 ) ( ) ( n s n s x x + - - - μ μ This will have the standard t distribution if 1 σ = 2 σ Example: 1 x = 84 2 x = 91 n 1 = 16 n 2 = 16 s 1 = 8 s 2 = 4 test: Ho: μ 1 = μ 2 Ha: μ 1 < μ 2 α = .05

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TI: 2-SamptTest PHStat: Two sample test for the mean, 1 σ and/or 2 σ unknown PHStat t Test for Differences in Two Means Data
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