12.1 - I independent random samples of sizes n 1 n 2 … n...

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Unformatted text preview: I independent random samples of sizes n 1 , n 2 , … , n I , each from a normal distribution Pooled two sample t-test To test the hypothesis H : µ 1 = µ 2 against the two-sided alternative, use the pooled two-sample t statistic How do we compare several means? We want to know if the observed differences in sample means are likely to have occurred by chance just because of the random sampling. This will likely depend on both the difference between the sample means and how much variability there is within each sample. Do nematodes affect plant growth? A botanist prepares 16 identical planting pots and adds different numbers of nematodes into the pots. Seedling growth (in mm) is recorded two weeks later. Nematodes and plant growth Nematodes 0 10.8 9.1 13.5 9.2 10.65 1,000 11.1 11.1 8.2 11.3 10.43 5,000 5.4 4.6 7.4 5 5.6 10,000 5.8 5.3 3.2 7.5 5.45 Seedling growth overall mean 8.03 € x i Hypotheses: All μ i are the same ( H ) versus not all μ i are the same ( H a ) Need a measure of the differences among the sample means as well as a measure of the variability within samples. Nematodes 0 10.8 9.1 13.5 9.2 10.65 1,000 11.1 11.1 8.2 11.3 10.43 5,000 5.4 4.6 7.4 5 5.6 10,000 5.8 5.3 3.2 7.5 5.45 Seedling growth overall mean 8.03 € x i SSG = 4(10.65 – 8.03) 2 + 4(10.43 – 8.03) 2 + 4(5.6 – 8.03) 2 + 4(5.45 – 8.03) 2 = 100.647 SSE = (10.8 – 10.65) 2 + (9.1 – 10.65) 2 + (13.5 – 10.65) 2 + (9.2 – 10.65) 2 + ………….....
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12.1 - I independent random samples of sizes n 1 n 2 … n...

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