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A textile mill company is investigating a new drapery yarn, which the company claims have a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho: u = 12 against H;: µ+ 12, using a random sample of four specimens.

A textile mill company is investigating a new drapery yarn, which the company claims have a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho: u = 12 against H;: µ+ 12, using a random sample of four specimens.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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A textile mill company is investigating a new drapery yam, which the company claims have a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho: µ = 12 against H;: µ # 12, using a random sample of four specimens. v What is the type I error probability if the acceptance region is 11.4 < iS 12.6 ? a. P(Type I Error) = 0.0082 b.n z4 specimens c. P(Type I error) = 0.0164 -v If a = 0.05, would we need to reject the H,? d. P(Type II Error) = 0.34 v Find B for the case in which the true mean elongation is 12.70 kilograms e, Cannot determine choice of sample size f. Reject Ho. The mean thread elongation is not 12 kilograms v Find n if the company wishes to detect that the mean thread elongation is not equal to 12 kilograms at g. B = 0.6554 least 80% of the time h. Fail to reject Ho- The mean thread elongation is equal to 12 kilograms, per significance level of 0.05 and 4 specimens collected
Transcribed Image Text:A textile mill company is investigating a new drapery yam, which the company claims have a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho: µ = 12 against H;: µ # 12, using a random sample of four specimens. v What is the type I error probability if the acceptance region is 11.4 < iS 12.6 ? a. P(Type I Error) = 0.0082 b.n z4 specimens c. P(Type I error) = 0.0164 -v If a = 0.05, would we need to reject the H,? d. P(Type II Error) = 0.34 v Find B for the case in which the true mean elongation is 12.70 kilograms e, Cannot determine choice of sample size f. Reject Ho. The mean thread elongation is not 12 kilograms v Find n if the company wishes to detect that the mean thread elongation is not equal to 12 kilograms at g. B = 0.6554 least 80% of the time h. Fail to reject Ho- The mean thread elongation is equal to 12 kilograms, per significance level of 0.05 and 4 specimens collected
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