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IE4521_HW5b_Solution

# IE4521_HW5b_Solution - 8.1.2 With to.005,4o = 2.704 the...

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Unformatted text preview: 8.1.2 With to.005,4o = 2.704 the conﬁdence interval is 2.704X0.124 I 2.704 0.124 _ (3.04 m ,3.04. 5% )_(2.99,3.09). The conﬁdence interval does not contain the value 2.90, and so 2.90 is not a plausible value for the mean glass thickness. 8.1.5 With 20325 = 1.960 the conﬁdence interval is 1.960X0.015 1.960X0.015 _ (0.0328 — T,0.0328 + T) _ (0027200384). 8.1.9 A total sample size of to.025,n1—1 5 2 is required. Therefore, an additional sample of at least 39 — 31 = 8 observations should be sufﬁcient. 8.2.3 (a) The test statistic is z = Jaime) = v’ﬁxgagSQ—aul = 1.3% The p—value is 2 X @(—1.34) = 0.180. (b) The test statistic is _ ﬁﬁ— ) _ «Exams—3.1) _ 2— or m — 0.325 — 2'45‘ The p—value is lI)(—2.45) = 0.007. 8.2.7 (a) The critical point is £33545 2 1.753 and the null hypothesis is accepted when [ti 5 1.753. (b) The critical point is to_005,15 = 2.947 and the null hypothesis is rejected when It] > 2.947. (c) The test statistic is f'— ME 1.053—1.025 t: ”(38 “0): “[1058 J21.931. The null hypothesis is rejected at size or = 0.10 and accepted at size a = 0.01. (d) The p—value is 2 X P(t15 2 1.931) = 0.073. 8.2.9 (a) The critical point is £313,543 2 1.296 and the null hypothesis is accepted when t g 1.296. (b) The critical point is 3001,60 = 2.390 and the null hypothesis is rejected when t > 2.390. (c) The test statistic is _ ﬁrs— ) _ Jﬁx(o.07ss—0.065) _ t — S “'0 — [10231 — 3.990. The null hypothesis is rejected at size or = 0.01 and consequently also at size a = 0.10. (d) The p—value is P(t50 2 3.990) = 0.0001. 8.2.11 Consider the hypotheses H0 : p = 44.350 versus HA : ,1; 7E 44.350. The test statistic is .5 e— m 44364—44350 t = (s “0) = X‘ mg l = 3.61. The p—value is 2 X P(t23 2 3.61) = 0.0014. There is sufﬁcient evidence to conclude that the machine is miscahbrated. 8.2.15 Consider the hypotheses H0 : ,u. <_: 2.5 versus HA :p. > 2.5. The test statistic is f2 x/E 2.752—25 [email protected]=%=2-S4ﬂ The p—value is P(tg 2 2.846) : 00096. There is sufﬁcient evidence to conclude that the average corrosion rate of chilled cast iron of this type is larger than 2.5. 8.5.11 At a 95% conﬁdence level the critical points are X51125,” = 30-19 and X%.975,17 = 7.564 so that the conﬁdence interval is 13—1 (-3.432 18—1 6.489 (( 3d.)1(9 *( 735;; )=(23.6,94.4), At a 99% conﬁdence level the critical points are X30054? 2 3572 331d Xﬁ.995,17 = 5.697 so that the conﬁdence interval is 13—1 x6482 13—1 x6432 (( 3:172 J 52597 )=(20.0,125.3). 8-5-13 At a 95% conﬁdence level the critical points are \$1125.19 = 32-85 311d 363975,ng = 8.907 so that the conﬁdence interval is 20—1 11.9439 20—1 11.913“2 (( 3535 .( £537 )=(81.9,302.1)_ ...
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