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# 05 level the table says we need 10 or less note data

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05 level (the table says we need 10 or less). Note: data set 3 returns p > . 05 with a t-test because the variability in sample “b” is large. Data set 4 also returns p > . 05 with a t-test because the difference in sample means is small. (c) For data set 3, Mann-Whitney test would be most appropriate, because we are not sure the data are normally 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 powerful than Mann-Whitney test when both can be used. 3(a) Smaller with a one-sided test in the correct direction. The formula for n is σ 2 ( z α/ 2 + z β ) 2 / ( μ 0 - μ a ) 2 for a 2-sided test, while we replace z α/ 2 = z . 015 = 2 . 17 by z α = z . 03 = 1 . 88 for a one-sided test. z α being smaller, n is also smaller for a one-sided test. (b) Using n = σ 2 ( z α/ 2 + z β ) 2 / ( μ 0 - μ a ) 2 we get 25 = 104 * (2 . 17 + z β ) 2 / (0 - 5) 2 i.e. z β = 6 . 01 - 2 . 17 = 0 . 281 and with Table A β = . 3897 so the power is 61%. One can get the same result by determining the
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