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Cereal boxes ~ A large box of corn flakes claims to contain 525 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 531 grams in each box. The machine has a known standard deviation of 3 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 5 boxes and weigh the cereal in each box. If the average is less than 525 grams, the machine is shut down and adjusted. 1. How often will the workers make a Type I error with this decision rule and the hypotheses: Ho : µ = 531 vs. H. : µ < 531 Probability of a Type I error = 2. Arka and Sikta both work at the plant and are dissatisfied by the Type I error rate in part 1. Arka argues the decision rule should be changed such that workers will only shut down the factory if the average is less than 521 grams. Sikta believes the plant should keep the same decision rule, but sample 11 boxes for each quality control check, rather than only 5. Which option will result in a smaller Type I error rate? v? Arka's option 3. L iesis test if the machine is actually filling boxes with an average of 525 grams? That is, Sikta's option calc 21 if the true mean is 525. Both options give the same Type I error rate

Cereal boxes ~ A large box of corn flakes claims to contain 525 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 531 grams in each box. The machine has a known standard deviation of 3 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 5 boxes and weigh the cereal in each box. If the average is less than 525 grams, the machine is shut down and adjusted. 1. How often will the workers make a Type I error with this decision rule and the hypotheses: Ho : µ = 531 vs. H. : µ < 531 Probability of a Type I error = 2. Arka and Sikta both work at the plant and are dissatisfied by the Type I error rate in part 1. Arka argues the decision rule should be changed such that workers will only shut down the factory if the average is less than 521 grams. Sikta believes the plant should keep the same decision rule, but sample 11 boxes for each quality control check, rather than only 5. Which option will result in a smaller Type I error rate? v? Arka's option 3. L iesis test if the machine is actually filling boxes with an average of 525 grams? That is, Sikta's option calc 21 if the true mean is 525. Both options give the same Type I error rate

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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Cereal boxes A large box of corn flakes claims to contain 525 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 531 grams in each box. The machine has a known standard deviation of 3 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 5 boxes and weigh the cereal in each box. If the average is less than 525 grams, the machine is shut down and adjusted. 1. How often will the workers make a Type I error with this decision rule and the hypotheses: Но : и 3D 531 vs. Ha : и< 531 Probability of a Type I error = 2. Arka and Sikta both work at the plant and are dissatisfied by the Type I error rate in part 1. Arka argues the decision rule should be changed such that workers will only shut down the factory if the average is less than 521 grams. Sikta believes the plant should keep the same decision rule, but sample 11 boxes for each quality control check, rather than only 5. Which option will result in a smaller Type I error rate? v? Arka's option 3. U iesis test if the machine is actually filling boxes with an average of 525 grams? That is, Sikta's option calc 21 if the true mean is 525. Both options give the same Type I error rate TUWCI -
Transcribed Image Text:Cereal boxes A large box of corn flakes claims to contain 525 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 531 grams in each box. The machine has a known standard deviation of 3 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 5 boxes and weigh the cereal in each box. If the average is less than 525 grams, the machine is shut down and adjusted. 1. How often will the workers make a Type I error with this decision rule and the hypotheses: Но : и 3D 531 vs. Ha : и< 531 Probability of a Type I error = 2. Arka and Sikta both work at the plant and are dissatisfied by the Type I error rate in part 1. Arka argues the decision rule should be changed such that workers will only shut down the factory if the average is less than 521 grams. Sikta believes the plant should keep the same decision rule, but sample 11 boxes for each quality control check, rather than only 5. Which option will result in a smaller Type I error rate? v? Arka's option 3. U iesis test if the machine is actually filling boxes with an average of 525 grams? That is, Sikta's option calc 21 if the true mean is 525. Both options give the same Type I error rate TUWCI -
Cereal boxes - A large box of corn flakes claims to contain 525 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 531 grams in each box. The machine has a known standard deviation of 3 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 5 boxes and weigh the cereal in each box. If the average is less than 525 grams, the machine is shut down and adjusted. 1. How often will the workers make a Type I error with this decision rule and the hypotheses: Но : и 3D 531 vs. Ha : и < 531 Probability of a Type I error = 2. Arka and Sikta both work at the plant and are dissatisfied by the Type I error rate in part 1. Arka argues the decision rule should be changed such that workers will only shut down the factory if the average is less than 521 grams. Sikta believes the plant should keep the same decision rule, but sample 11 boxes for each quality control check, rather than only 5. Which option will result in a smaller Type I error rate? ? 3. Using Arka's decision rule, what is the power of the hypothesis test if the machine is actually filling boxes with an average of 525 grams? That is, calculate the chance of observing a sample mean less than 521 if the true mean is 525. Power =
Transcribed Image Text:Cereal boxes - A large box of corn flakes claims to contain 525 grams of cereal. Since cereal boxes must contain at least as much product as their packaging claims, the machine that fills the boxes is set to put 531 grams in each box. The machine has a known standard deviation of 3 grams and the distribution of fills is known to be normal. At random intervals throughout the day, workers sample 5 boxes and weigh the cereal in each box. If the average is less than 525 grams, the machine is shut down and adjusted. 1. How often will the workers make a Type I error with this decision rule and the hypotheses: Но : и 3D 531 vs. Ha : и < 531 Probability of a Type I error = 2. Arka and Sikta both work at the plant and are dissatisfied by the Type I error rate in part 1. Arka argues the decision rule should be changed such that workers will only shut down the factory if the average is less than 521 grams. Sikta believes the plant should keep the same decision rule, but sample 11 boxes for each quality control check, rather than only 5. Which option will result in a smaller Type I error rate? ? 3. Using Arka's decision rule, what is the power of the hypothesis test if the machine is actually filling boxes with an average of 525 grams? That is, calculate the chance of observing a sample mean less than 521 if the true mean is 525. Power =
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