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ViG a large manof actuer 2.45 Ln order to meet tighte speficatians cagineers are trying to reduce the Naiablt ofte protess A
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Answer #1

Given : Sample size=n=28

Sample standard deviation=s=2.65

Hypothesis : Ho : σ = 2.95 VS H, : σ < 2.95

The test statistic under Ho is,

x2 = (n - 1) 2

(28 - 1)2.652 2,052 21.79

A) For a-0.05

Critical value = la,n-l 2 -10.05.27-40.113 a,n-1 Χο.05.27 40,113 _ ; from excel "=CHIINV(0.05,27)"

Decision : Here , Xstat -21.79 < Xa,n40.113

Therefore , fail to reject Ho at 5% significance level.

Conclusion : Hence , there is not sufficient evidence to conclude that the standard deviation has decreased.

B) For α 0.01

Critical value = χ0.01 .27 _ a,n-1 46.963 ; from excel "=CHIINV(0.01,27)"

Decision : Here , Xstat -21.79 < Xa,n46.963

Therefore , fail to reject Ho at 1% significance level.

Conclusion : Hence , there is not sufficient evidence to conclude that the standard deviation has decreased.

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