GATE (TF) Textile 2009 Question Paper Solution | GATE/2009/TF/49

Question 49 (Textile Engineering & Fibre Science)

99% confidence range of the mean yarn strength based on 64 test samples is $\pm$ 8. The number of test samples required to obtain 99% confidence rage of 4 $\pm$ of the yarn strength will be

(A)	64
(B)	128
(C)	256
(D)	512

[Show Answer]

Option C is correct

Given-

99% confidence range

No. of samples(N1)=64

Confidence range of mean yarn strength(R1)=8

No. of sample(N2)=?

Confidence range of mean yarn strength(R2)=4

By formula-

$No. of samples=\frac{2.56 \times CV percentage}{S.E.}^2$

$No. of samples=\frac{2.56 \times CV}{S.E.}^2$

Confidence range(R)=2.56 x Standard error(S.E)

$No. of sample \Alpha \frac{1}{S.E.^2}$

i.e.

$No. of sample \Alpha \frac{1}{R^2}$

$\frac{N_1}{N_2}=\frac{R_2^2}{R_1^2}$

$\frac{64}{N_2}=\frac{4^2}{8^2}$

$\frac{64}{N_2}=\frac{16}{64}$

$N_2=\frac{64}{16} \times 64$

$N_2=256$ (Ans)

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