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# PS7s - SOLUTIONS TO ISMT111 PROBLEM SET#7(1 Answer(D Do not...

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SOLUTIONS TO ISMT111 PROBLEM SET #7 (1) Answer: (D) Do not reject H o at the .005 level but reject H o at the .01 level. Left-tailed test. n = 24 (small), X = 0 . 95, S = 0 . 36. σ unknown, X is normal. t obs = x obs - μ o S/ n = 0 . 95 - 1 . 15 0 . 36 / 24 = - 2 . 7216 ( df = 23) d.f. α = . 01 p α = . 005 x x x 23 -→ 2.500 ( t obs = 2 . 7216) 2.807 one sided : . 01 > p > . 005 Answer is (D) since the null is rejected only if α > p -value . (2) Answer: 0.0228 n = 4 (small), X = 245, S = 6 . 2, σ = 5 (known), X is normal. To test H o : μ = 240 vs. H a : μ > 240; (right-tailed); z obs = x obs - 240 σ/ n = 245 - 240 5 / 4 = 2 . From z-table, the right-tailed area beyond a z obs of 2 is . 0228 (= . 5 - . 4772). For a one-tailed test, p = . 0228. (3) (a) Either a Type I or Type II error could have been committed but not both. (F) (b) A Type I error could not have been committed. (T) (c) The p -value is greater than the signiﬁcance level of α . (T) (d) A Type II error could have been committed. (T)

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PS7s - SOLUTIONS TO ISMT111 PROBLEM SET#7(1 Answer(D Do not...

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