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A company is experimenting with synthetic fibers as a substitute for natural fibers. The quality characteristic of...

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Basic Math

A company is experimenting with synthetic fibers as a substitutefor natural fibers.

The quality characteristic of interest is the breaking strength.A random sample of 8 natural fibers yields an average breakingstrength of 540 kg with a standard deviation of 55 kg. A randomsample of 10 synthetic fibers gives a mean breaking strength of 610kg with a standard deviation of 22 kg.

(a) Can you conclude that the variances of the breakingstrengths of natural and synthetic fibers are different? Use alevel of significance α of 0.05.

(b) Find a two-sided 95% confidence interval for the ratio ofthe variances of the breaking strengths of natural and syntheticfibers.

Answer & Explanation Solved by verified expert
3.8 Ratings (353 Votes)
a For this we conduct an F test for 2 variances Since we wantto test variationGivens1 55 s12 3025n1 8 df1 81 7s2 22 s22 484n2 10 df2 101 9TheHypothesisH0 There is no difference in variances of the breaking    See Answer
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