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**Unformatted text preview: **Two-Sample Z-Tests If the samples are large, random, and independent, then is a random variable and has approximately a normal distribution, with So, However, since H is usually 1 = 2 , then 1- 2 =0 and: for 1 , 2 known for 1 , 2 unknown Z = if n 1 + n 2 32 For a 1- % Confidence Interval for the difference between two means: When we construct the confidence interval for the mean difference in the population ( 1- 2 ), we check to see whether 0 is in the interval. If 0 is in the interval, then we are basically saying that there may be no difference between the two groups and the observed difference between the two sample means is simply sampling error. The Null hypothesis that 1 = 2 , is the same as saying that the hypothesized mean difference is 0, i.e., ( 1- 2 ) = 0. EXAMPLE: Compare the following 2 groups Drug Group Placebo Group 1 = 4.4 colds 2 = 4.8 colds S 1 = 0.7 colds S 2 = 0.8 colds n 1 = 81 n 2 = 64 (a) Test at = .05 (these tests are usually two-tailed) REJECT H [Therefore, REJECT H p < .05.] (b) Construct a 95% Confidence Interval Estimate for the difference between the...

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