GATE (TF) Textile 2006 Question Paper Solution | GATE/2006/TF/57

One hundred 1.5 dtex polyester fibres with density of 1.35 g/cm3 are tested on a CRE tensile tester. 95% confidence range of main tensile properties are follows
Tenacity (gf/tex): 35 \pm 5.32
Elongation (%) : 30 \pm 7
Initial Modulus (gf/tex) : 35 \pm 9

Question 57 (Textile Engineering & Fibre Science)

99% confidence range of tenacity in gf/tex is

(A)35 \pm 9
(B)35 \pm 5
(C)35 \pm 7
(D)35 \pm 9
[Show Answer]

Option C is correct.
95% confidence range of main tensile properties are follows
Tenacity (gf/tex): 35 \pm 5.32
Elongation (%) : 30 \pm 7
Initial Modulus (gf/tex) : 35 \pm 9

Now, find 99% confidence range tenacity in gf/tex=?

Let, S.E(standard error at 95% confidence interval of tenacity)=S.E_1=5.32

S.E(standard error at 99% confidence interval of tenacity)=S.E_2

By formula in 95% confidence range-

N=(\frac{1.96 \times \S.D}{S.E_1})^2……………………(1)

Formula in 99% confidence range-

N=(\frac{2.56 \times \S.D}{S.E_2})^2…………………..(2)

Divide both the equations-

1=(\frac {1.96 \times S.E_2}{2.56 \times S.E_1})^2

1=\frac {1.96 \times S.E_2}{2.56 \times S.E_1}

\frac{S.E._1 \times 2.56}{1.96}=S.E._2

S.E._2=\frac{5.32 \times 2.56}{1.96}

S.E._2=6.95

S.E._2=7

Now,

99% confidence range tenacity in gf/tex=35\pm S.E._2

99% confidence range tenacity in gf/tex=35\pm7 (Ans)

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