GATE (TF) Textile 2006 Question Paper Solution | GATE/2006/TF/58

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 58 (Textile Engineering & Fibre Science)

If 38% confidence range elongation (%) with same error percentage is required to be 30 $\pm$ 9, the number of samples required to be tested is

(A)	99
(B)	129
(C)	149
(D)	169

[Show Answer]

Given-
At 95% confidence range-
S.E._1=7

N1=100

By formula-

$N=(\frac{1.96 \times CV}{S.E._1})^2$

$100=(\frac{1.96 \times CV}{7})^2$

$10=\frac{1.96 \times CV}{7}$

$CV=\frac{10 \times 7}{1.96}$

$CV=\frac{70}{1.96}$

CV=35.71

Again,

S.E_2=5

N_2=?

$N_2=(\frac{1.96 \times CV}{S.E._2})^2$

$N_2=(\frac{1.96 \times 35.71}{5})^2$

$N_2=(\frac{70}{5})^2$

$N_2=(14)^2$

$N_2=196$ (Ans)

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