## Answers

let, P- the pooportion of porosity of a certain seara, no.

Of helium porosity of a certain seam. out 01 n 20, Here, p=² @ Here given, that (60%) 9 21:P = 0.4 9% have to computea confidence interval for the true proportion the true proportion porosity of certain 99% seam. given that, significance level (2)=0.01 0.01 (1) 3 The required confidence intervall is, C P-2d/2 P=2016 F Pg Pt 2212 P9 р 2212= Zo.01 2.58 0.6 - 2.58 0.6x04 0.6t 2.58 o 67004 2oo 0.51 0. 69 2 ( Here the margin of error (MoE is MO 2012 pq D CS Samuel Wick CAMSCANNER

MoE = 2.58 200 rimo E = o. 68937 moe seam Claim: IS to be tested, the true proportion porosity of am certain is more than 0.65 Here, the specified value of P = Po - 0.65 Po= |- Po=0.35 i) To test, Hou p = 0.65 Hp: P >0.65 us ii) Test statistic, Zcal P-Po Pogo NNLOAD under Ho 0.6-0.65.

0.65 X 0.35 200 .:2cal -1.48 Hi given that, signifiance level (d) = o.of (1% Critical value = 20.01 Z2 = cs

Page iv) Decision criteria : We reject to at L .l. level of signifi cance Here Z call 7 Zd acal za te - 1.48 K 2-33 accept to at 17 level of significanie - Conclusion: Since, the test statistic is less than the critical value we have enough evidence, +0 conclude that the pro portion porosity of a certain seam is more than 0.55 d @ Here, we have to find sample size (3) Decessary in the marginal error of the 99 % interval is to be 0016. 0.016 2212 pg n 2.58 0.6x0.4 -0.016 1.2639 1,2639 T5 = 78.99 60 n = (7869960)2 6240.375 nr 6240 n ..The required sample size is co] 6240 csl

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