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ms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis random sample of 4 specimens. your answers to 4 decimal places. at is the type I error probability if the critical region is defined as < 11.5 kilograms? De l error probability is 0.0228 d for the case where the true mean elongation is 11.27 kilograms.

ms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis random sample of 4 specimens. your answers to 4 decimal places. at is the type I error probability if the critical region is defined as < 11.5 kilograms? De l error probability is 0.0228 d for the case where the true mean elongation is 11.27 kilograms.

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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**Textile Fiber Manufacturer Hypothesis Testing** A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis \( H_0: \mu = 12 \) against \( H_1: \mu < 12 \), using a random sample of 4 specimens. Round your answers to 4 decimal places. (a) **Type I Error Probability** What is the type I error probability if the critical region is defined as \( \bar{x} < 11.5 \) kilograms? - The type I error probability is \( 0.0228 \). (b) **Type II Error Probability Calculation (\(\beta\))** Find \( \beta \) for the case where the true mean elongation is 11.27 kilograms. - \( \beta = 0.1011 \) (c) **Type II Error Probability Calculation (\(\beta\))** Find \( \beta \) for the case where the true mean is 11.5 kilograms. - \( \beta = 0.3612 \) **Additional Information:** - Statistical Tables and Charts are used to calculate these probabilities.
Transcribed Image Text:**Textile Fiber Manufacturer Hypothesis Testing** A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis \( H_0: \mu = 12 \) against \( H_1: \mu < 12 \), using a random sample of 4 specimens. Round your answers to 4 decimal places. (a) **Type I Error Probability** What is the type I error probability if the critical region is defined as \( \bar{x} < 11.5 \) kilograms? - The type I error probability is \( 0.0228 \). (b) **Type II Error Probability Calculation (\(\beta\))** Find \( \beta \) for the case where the true mean elongation is 11.27 kilograms. - \( \beta = 0.1011 \) (c) **Type II Error Probability Calculation (\(\beta\))** Find \( \beta \) for the case where the true mean is 11.5 kilograms. - \( \beta = 0.3612 \) **Additional Information:** - Statistical Tables and Charts are used to calculate these probabilities.
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