# Difference between population means two sided

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difference between population means Two-sided: Question just asks about any difference H 0 : 1 = 2 H 0 : 1 2 = 0 All are contradicted by the same null hypothesis
0 : H 0 wsu uw 0 : H a wsu uw Set up a test assuming that the null (H O ) is true and see whether the facts of our sample contradict that assumption. Key question: How likely is it that we would observe a sample difference (14.5-12.5 = 2 hrs) if the null (H O ) were true? If very unlikely, we will reject H O and support H a If not very unlikely, we will fail to reject H O Two-sample hypothesis test We want to know if UW students differ from WSU students in terms of average study time. We draw a random sample of 100 UW students and find an average study time of 14.5 hours per week with a standard deviation of 8.25. In contrast, our sample of 81 WSU students has an average study time of 12.5 hours per week with a standard deviation of 7.0. Use a .05 alpha level to test the statistical significance of the observed difference between means. Plan: State the HYPOTHESES
0 : H 0 wsu uw 0 : H a wsu uw Set up a test assuming that the null (H O ) is true and see whether the facts of our sample contradict that assumption. Key question: How likely is it that we would observe a sample difference (14.5-12.5 = 2 hrs) if the null (H O ) were true? If very unlikely, we will reject H O and support H a If not very unlikely, we will fail to reject H O Have to think about probability of receiving our sample result (difference) if H 0 were true Have to think about the SAMPLING DISTRIBUTION of all possible sample results Plan: State the HYPOTHESES Two-sample hypothesis test
Sampling theory: Hypothesis test for difference between means Sampling Distribution for the difference between means A theoretical probability distribution that would be obtained by calculating all of the possible mean differences ( ) for all possible pairs of random, independent samples of size n 1 and n 2 drawn from two populations. 2 1 X X
Characteristics of the Sampling Distribution for Difference between Two Means: IF the random samples are independently drawn AND the sample sizes are large (n 1 + n 2 > 100) then: The sampling distribution of differences between means would be NORMAL [but use the t-distribution when population standard deviations are unknown] The MEAN of this distribution would equal the real difference between the population means The STANDARD ERROR of the sampling distribution of differences would be equal to: 2 2 2 1 2 1 2 1 n n X X 2 1 2 1 X X 2 2 2 1 2 1 2 1 n s n s s X X ESTIMATE Sampling theory: Hypothesis test for difference between means
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