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A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: u = 175 millimeters versus H1: µ + 175 millimeters, using the results of n = 10 samples.

A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: u = 175 millimeters versus H1: µ + 175 millimeters, using the results of n = 10 samples.

MATLAB: An Introduction with Applications
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 consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: µ = 175 millimeters versus H1: µ + 175 millimeters, using the results of n = 10 samples. What is the type I error probability if the acceptance region is 155 sis 195? a. Reject Ho b. P(Type II Error) = 0.5 v If a = 0.05, would we need to reject the Ho? c. Probability of committing Type I Error cannot be determined because a was not given Find ß for the case in which the true foam height is 156 millimeters d. n should be lower than 10 samples e. P(155 <x< 195, when µ=156) = 0.5628 Find n if fhe protubily of failing lo rejecti a false sall hypelhenis is sel al 0.0S. And that fle true fiam aeighr. was found to be really 156 millimetes f. Fail to reject Ho. The 10 samples may not be an appropriate sample size g.n z 14 h. P(Type I Error) = 0.00157 %3D
Transcribed Image Text:A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately normally distributed and has a standard deviation of 20 millimeters. The company wishes to test Ho: µ = 175 millimeters versus H1: µ + 175 millimeters, using the results of n = 10 samples. What is the type I error probability if the acceptance region is 155 sis 195? a. Reject Ho b. P(Type II Error) = 0.5 v If a = 0.05, would we need to reject the Ho? c. Probability of committing Type I Error cannot be determined because a was not given Find ß for the case in which the true foam height is 156 millimeters d. n should be lower than 10 samples e. P(155 <x< 195, when µ=156) = 0.5628 Find n if fhe protubily of failing lo rejecti a false sall hypelhenis is sel al 0.0S. And that fle true fiam aeighr. was found to be really 156 millimetes f. Fail to reject Ho. The 10 samples may not be an appropriate sample size g.n z 14 h. P(Type I Error) = 0.00157 %3D
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