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: µ = 12 against H1: µ # 12, using a random sample of four specimens. %3D
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: µ = 12 against H1: µ # 12, using a random sample of four specimens. %3D
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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: µ = 12 against H;: µ # 12, using a random sample of four specimens.
What is the type I error probability if the acceptance region is 11.4 s iS 12.6 ? a. ß = 0.6554
b. P(Type I error) = 0.0164
c. P(Type II Error) = 0.34
v If a = 0.05, would we need to reject the Ho?
d. Reject Ho. The mean thread elongation is not 12 kilograms
v Find B for the case in which the true mean elongation is 12.70 kilograms
e. P(Type I Error) = 0.0082
f. Cannot determine choice of sample size
v Find n if the company wishes to detect that the mean thread elongation is not equal to 12 kilograms at g. Fail to reject Ho. The mean thread elongation is equal to 12 kilograms, per
least 80% of the time
significance level of 0.05 and 4 specimens collected
h.n z 4 specimens](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fec6745c0-dd5c-40c0-93fe-e835c814a18b%2F6b1d256d-d033-477d-ae89-cdaaca282b3f%2F0rffxth_processed.png&w=3840&q=75)
Transcribed Image Text: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: µ = 12 against H;: µ # 12, using a random sample of four specimens.
What is the type I error probability if the acceptance region is 11.4 s iS 12.6 ? a. ß = 0.6554
b. P(Type I error) = 0.0164
c. P(Type II Error) = 0.34
v If a = 0.05, would we need to reject the Ho?
d. Reject Ho. The mean thread elongation is not 12 kilograms
v Find B for the case in which the true mean elongation is 12.70 kilograms
e. P(Type I Error) = 0.0082
f. Cannot determine choice of sample size
v Find n if the company wishes to detect that the mean thread elongation is not equal to 12 kilograms at g. Fail to reject Ho. The mean thread elongation is equal to 12 kilograms, per
least 80% of the time
significance level of 0.05 and 4 specimens collected
h.n z 4 specimens
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