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14. A potato chip manufacturer regularly inspects bags of chips to make sure there aren't too many below the advertised weight of 32 ounces. Each hour they take a random sample of 10 bags of chips, calculate the first quartile (Q.) for the sample of weights, and adjust the machine if Q, is significantly less than 32 ounces. (a) Define the parameter of interest and state the hypotheses the manufacturer wants to test. Q1 = H,: H : Here are the weights of 10 bags from one random sample. Bag Number Weight (ounces) 31.1 | 31.8 34.6 33..3 29.9 30.2 321 326 31.9 31.2 2. 3 4. 6. 8. 9. 10

14. A potato chip manufacturer regularly inspects bags of chips to make sure there aren't too many below the advertised weight of 32 ounces. Each hour they take a random sample of 10 bags of chips, calculate the first quartile (Q.) for the sample of weights, and adjust the machine if Q, is significantly less than 32 ounces. (a) Define the parameter of interest and state the hypotheses the manufacturer wants to test. Q1 = H,: H : Here are the weights of 10 bags from one random sample. Bag Number Weight (ounces) 31.1 | 31.8 34.6 33..3 29.9 30.2 321 326 31.9 31.2 2. 3 4. 6. 8. 9. 10

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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14. A potato chip manufacturer regularly inspects bags of chips to make sure there aren't too many below the advertised weight of 32 ounces. Each hour they take a random sample of 10 bags of chips, calculate the first quartile (Q.) for the sample of weights, and adjust the machine if Q, is significantly less than 32 ounces. (a) Define the parameter of interest and state the hypotheses the manufacturer wants to test. Q1 = bns H,: Here are the weights of 10 bags from one random sample. Bag Number 1. 3 5 6. 7. 8. 9. 10 Weight (ounces) 31.1 31.8 34.6 33.3 29.9 30.2 32.1 32.6 31.9 31.2 (b) State the evidence for the alternative hypothesis provided by these data. (c) Is it plausible that the population of bag weights is approximately Normally distributed? Explain. (d) A simulation was conducted where 100 random samples of size 10 were generated from a Normal population where the value of Q. was 32. The sample Qi for each of these samples was computed and is displayed below. Use the results of this simulation to test the hypotheses in part (a). 29.5 300 30.5 31.0 31.5 32.0 325 330 33.5 Simulated Sample Qs
Transcribed Image Text:14. A potato chip manufacturer regularly inspects bags of chips to make sure there aren't too many below the advertised weight of 32 ounces. Each hour they take a random sample of 10 bags of chips, calculate the first quartile (Q.) for the sample of weights, and adjust the machine if Q, is significantly less than 32 ounces. (a) Define the parameter of interest and state the hypotheses the manufacturer wants to test. Q1 = bns H,: Here are the weights of 10 bags from one random sample. Bag Number 1. 3 5 6. 7. 8. 9. 10 Weight (ounces) 31.1 31.8 34.6 33.3 29.9 30.2 32.1 32.6 31.9 31.2 (b) State the evidence for the alternative hypothesis provided by these data. (c) Is it plausible that the population of bag weights is approximately Normally distributed? Explain. (d) A simulation was conducted where 100 random samples of size 10 were generated from a Normal population where the value of Q. was 32. The sample Qi for each of these samples was computed and is displayed below. Use the results of this simulation to test the hypotheses in part (a). 29.5 300 30.5 31.0 31.5 32.0 325 330 33.5 Simulated Sample Qs
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