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Answers to Homework # 8 2. a) A larger difference will produce a larger value in the numerator which will produce a larger z-score b) A larger standard deviation will produce a larger standard error in the denominator which will produce a smaller z-score (more error) c) A larger sample will produce a smaller standard error in the denominator which will produce a larger z-score. 4. a) Lowering the alpha level causes the boundaries of the critical region to move farther out into the tails of the distribution. b) Lowering alpha reduces the probability of a Type I error. 6. a) I.V. = presence or absence of the training program D.V. = performance on the achievement test b) Null: states that the training program will have no effect on the scores on the achievement test c) H 0 : μ = 150 H 1 : μ ≠ 150 d) The critical region consists of z-score values beyond 1.96 and -1.96 in a normal distribution e) Z = M μ First calculate σ M = σ / √n = 25/5 = 5 158-150 = 1.60 σ M 5 f)

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