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# stat400sln11 - .4.“ 8.1—8 The value of the test...

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Unformatted text preview: .4...“- 8.1—8 The value of the test statistic ls z = 9.70 41.75 2 4.280. .f—Tm sj‘roan'mo (3) Since 2 = —2.280 < —1.645, reject 39. (b) Since 2 = —2.280 > —2.326, do not rqiect Ho. (c) p—value z P(Z 5 ~2.280) = 0.0113. Note that 0.01 < pmlue < 0.05. M“— ) 1.96- .,‘(uasjtossyn' ‘ ’ mime—0.65 .ﬂuosnossysoo (c) Since the p-value rs P(Z _>; 2.054) = 0.0200 < 0.0250, reject H9 at an a = 0.025 sigrﬁﬁcance level; 8.1—12 (a) z = (b) 2 = = 2.054 > 1.96, reject Ho at a = 0.025. 8.148 (3) Under Ho, 5: (351 + 41) 1300 = 0.49; lz|= I351/605—41/195l =[o.5so—-o.210|___8_99. 1 1 0.0412 (0.49)(0.51) (5T5 + 135—) Since 11.99 > 1.96, reject Ho. “0.58)(0.42) (021x039) (b) 0.58-0.21 :1: 1.96 T+T 0.37 :1: 1.96V0.000403+0.m51 0.37 :h 0.07 or [030,044]. It is in agreement with (3). 8.1—20 (a) z: 4:31—— > 1.645; V1311 - 131(1/1'11 + l/M} '- 0.15 -— 0.11 (1)) Z 2 mm = 2.34]. > 1.645, reject Ho. (c) z = 2.341 3- 2.326, reject Ho. ((1) The p—value a; P(Z 2 2.341) = 0.0096. 8.2—2 (3) The critical region is ”a? -- 10.1 t: > 1. . s/ﬂ— " 753 The observed value of t, 10.4 -— 10.1 ‘* 'TZ/T‘ _ 3-0! is greater that 1.753 so we reject Ho. (11} Since tomdlﬁ) = 2.947, the apprmdmate p-value of this test is 0.005. 4.5 3.2—4 (3.) m: [2010] a 0.025(9)=2.202. 0.4 Figure 8.2-4: The critical region is It] 2 2.262 (b) It] = w = 1.54 < 2.202, do not reject Ho. (c) A 95% conﬁdence interval for p is 0.1027 01027 155-0202 -——— 7.55+2.202 ——~ = 7.48, 7.02. i ( .00 ) ' ( «10 H ‘ 1 Hence, ,u = 7.50 is contained in this interval. We could have obtained the same conclusion from our answer to part (b). 8.2~—6 (a) Ho: p = 3.4; (b) HI: p > 3.4; (C) t = (i - 3-4)/(8/3); (d) t 2: 1.860; Figure 8.2-6: The critical region is t 2 1.860 3.556 - 3.4 0.107/3 (f) 2.802 > 1.860, reject Ha; .' (g) 0.01 < p—value < 0.025, pvalue = 0.0116. (e) t: = 2.802 ; a .2 . 3.2-10 (a) m = %J?:J 2mmu43-22J45. O. a . FEM 5.2—10: The critical region is Itl 2 2.1.45 IHWM 125] _ _ _ (b) ”I = lﬁlmi = 1.076 < 2.145. (10 not rqec—t Hg. ...
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stat400sln11 - .4.“ 8.1—8 The value of the test...

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