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To appeal to customers that are trying to cut calories, a company that sells orange juice decides to market a premium juice, "OJ 50", which has half as many calories as traditional orange juice. The ingredient listing reveals that OJ 50 consists of 50% water and 50% orange juice. Besides misleading customers to pay more for less orange juice, a consumer group believes that the product actually consists of greater than 50% water. To test this claim they select a random sample of 50 bottles of their 52-ounce ÕJ 50 and detemine the proportion of each that is water. They decide to use a=0.05. (a) State appropriate hypotheses for performing a significance test. (b) Describe what a Type I error would be in this context. (c) What is the probability of making a Type I error when perfoming this test? (4) Describe what a Type II error would be in this context. (e) Which error (Type I or Type II) is more serious for the company that produces OJ 50? Explain.

To appeal to customers that are trying to cut calories, a company that sells orange juice decides to market a premium juice, "OJ 50", which has half as many calories as traditional orange juice. The ingredient listing reveals that OJ 50 consists of 50% water and 50% orange juice. Besides misleading customers to pay more for less orange juice, a consumer group believes that the product actually consists of greater than 50% water. To test this claim they select a random sample of 50 bottles of their 52-ounce ÕJ 50 and detemine the proportion of each that is water. They decide to use a=0.05. (a) State appropriate hypotheses for performing a significance test. (b) Describe what a Type I error would be in this context. (c) What is the probability of making a Type I error when perfoming this test? (4) Describe what a Type II error would be in this context. (e) Which error (Type I or Type II) is more serious for the company that produces OJ 50? Explain.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 26EQ
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2. To appeal to customers that are trying to cut calories, a company that sells orange juice decides to market a premium juice, "OJ 50", which has half as many calories as traditional orange juice. The ingredient listing reveals that OJ 50 consists of 50% water and 50% orange juice. Besides misleading customers to pay more for less orange juice, a consumer group believes that the product actually consists of greater than 50% water. To test this claim they select a random sample of 50 bottles of their 52-ounce OJ 50 and detemine the proportion of each that is water. They decide to use a=0.05. (a) State appropriate hypotheses for performing a significance test. (b) Describe what a Type I error would be in this context. (c) What is the probability of making a Type I eror when performing this test? (d) Describe what a Type II error would be in this context. (e) Which error (Type I or Type II) is more serious for the company that produces OJ 50? Explain.
Transcribed Image Text:2. To appeal to customers that are trying to cut calories, a company that sells orange juice decides to market a premium juice, "OJ 50", which has half as many calories as traditional orange juice. The ingredient listing reveals that OJ 50 consists of 50% water and 50% orange juice. Besides misleading customers to pay more for less orange juice, a consumer group believes that the product actually consists of greater than 50% water. To test this claim they select a random sample of 50 bottles of their 52-ounce OJ 50 and detemine the proportion of each that is water. They decide to use a=0.05. (a) State appropriate hypotheses for performing a significance test. (b) Describe what a Type I error would be in this context. (c) What is the probability of making a Type I eror when performing this test? (d) Describe what a Type II error would be in this context. (e) Which error (Type I or Type II) is more serious for the company that produces OJ 50? Explain.
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