362 CHAPTER 7 Hypothesis Testing with One Sample Extending Concepts 53. Getting at the Concept Why can decreasing the probability of a type I error cause an increase in the probability of a type II error? 54. Getting at the Concept Explain why a level of significance of a = 0 is not used. 55. Writing A null hypothesis is rejected with a level of significance of 0.05. Is it also rejected at a level of significance of 0.10? Explain. 56. Writing A null hypothesis is rejected with a level of significance of 0.10. Is it also rejected at a level of significance of 0.05? Explain. Graphical Analysis In Exercises 57– 60, you are given a null hypothesis and three confidence intervals that represent three samplings. Determine whether each confidence interval indicates that you should reject H0. Explain your reasoning. 57. 67 68 69 70 71 72 73 μ H0: = 70 μ (a) 67 68 69 70 71 72 73 x 67 < < 71 μ (b) 67 68 69 70 71 72 73 x 67 < < 69 μ (c) 67 68 69 70 71 72 73 x < 72.5 69.5 < μ 58. 51 52 53 54 55 56 57 μ μ H0: ≤ 54 (a) 51 52 53 54 55 56 57 x < 56.5 53.5 < μ (b) 51 52 53 54 55 56 57 x < 54.5 51.5 < μ (c) 51 52 53 54 55 56 57 x < 55.5 54.5 < μ 59. 0.17 0.18 0.19 0.20 0.21 0.22 0.23 p H0: p ≤ 0.20 (a) 0.17 0.18 0.19 0.20 0.21 0.22 0.23 p 0.21 < p < 0.23 ˆ (b) 0.17 0.18 0.19 0.20 0.21 0.22 0.23 p 0.19 < p < 0.23 ˆ (c) 0.17 0.18 0.19 0.20 0.21 0.22 0.23 p 0.175 < p < 0.205 ˆ 60. 0.70 0.71 0.72 0.73 0.74 0.75 0.76 p H0: p ≥ 0.73 (a) 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.73 < p < 0.75 pˆ (b) 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.715 < p < 0.725 pˆ (c) 0.72 0.73 0.74 0.75 0.76 0.71 0.70 0.695 < p < 0.745 pˆ
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