05 level (the table sayswe need 10 or less). Note: data set 3 returnsp > .05with a t-test because the variability in sample “b” islarge. Data set 4 also returnsp > .05 with a t-testbecause the difference in sample means is small.(c) For data set 3, Mann-Whitney test would be mostappropriate, because we are not sure the data arenormally distributed (presence of an ’outlier’ in sam-ple “b”) and the sample size in each sample is small(4).For data set 4, a t-test would be most appro-priate, because the normal distribution seems appro-priate in each sample and the t-test is more powerfulthan Mann-Whitney test when both can be used.3(a) Smaller with a one-sided test in the correct direction.The formula fornisσ2(zα/2+zβ)2/(μ0-μa)2for a2-sided test, while we replacezα/2=z.015= 2.17byzα=z.03= 1.88 for a one-sided test.zαbeingsmaller,nis also smaller for a one-sided test.(b) Usingn=σ2(zα/2+zβ)2/(μ0-μa)2we get 25 =104*(2.17 +zβ)2/(0-5)2i.e.zβ=√6.01-2.17 =0.281 and with Table Aβ=.3897 so the power is61%. One can get the same result by determining the
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