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4. A production line is designed to fill cartons with detergent to a mean weight of 0.75 kg. A sample of cartons is periodically selected and weighed to determine whether under- filling or over-filling is occurring. If the sample data lead to a conclusion of under-filling or over-filling, the production line will be shut down and adjusted. Suppose a sample of n = 50 cartons yields a sample mean X = 0.743 kg. Assume the population standard deviation of carton weights is Psigma = 0.009 kg. Write the hypotheses test and compute the value of the test statistic. b. What is the p-value? c. At a = 0.01, what is your conclusion? d. What is a Type I error in this situation? What are the consequences of making this error? What is a Type ll error in this situation? What are the consequences of making this error?

4. A production line is designed to fill cartons with detergent to a mean weight of 0.75 kg. A sample of cartons is periodically selected and weighed to determine whether under- filling or over-filling is occurring. If the sample data lead to a conclusion of under-filling or over-filling, the production line will be shut down and adjusted. Suppose a sample of n = 50 cartons yields a sample mean X = 0.743 kg. Assume the population standard deviation of carton weights is Psigma = 0.009 kg. Write the hypotheses test and compute the value of the test statistic. b. What is the p-value? c. At a = 0.01, what is your conclusion? d. What is a Type I error in this situation? What are the consequences of making this error? What is a Type ll error in this situation? What are the consequences of making this error?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 14PPS
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4. A production line is designed to fill cartons with detergent to a mean weight of 0.75 kg. A sample of cartons is periodically selected and weighed to determine whether under- filling or over-filling is occurring. If the sample data lead to a conclusion of under-filling or over-filling, the production line will be shut down and adjusted. Suppose a sample of n = 50 cartons yields a sample mean X = 0.743 kg. Assume the population standard deviation of carton weights is Psigma = 0.009 kg. a. Write the hypotheses test and compute the value of the test statistic. b. What is the p-value? At a = 0.01, what is your conclusion? d. What is a Type I error in this situation? What are the consequences of making this error? What is a Type Il error in this situation? What are the consequences of making this error?
Transcribed Image Text:4. A production line is designed to fill cartons with detergent to a mean weight of 0.75 kg. A sample of cartons is periodically selected and weighed to determine whether under- filling or over-filling is occurring. If the sample data lead to a conclusion of under-filling or over-filling, the production line will be shut down and adjusted. Suppose a sample of n = 50 cartons yields a sample mean X = 0.743 kg. Assume the population standard deviation of carton weights is Psigma = 0.009 kg. a. Write the hypotheses test and compute the value of the test statistic. b. What is the p-value? At a = 0.01, what is your conclusion? d. What is a Type I error in this situation? What are the consequences of making this error? What is a Type Il error in this situation? What are the consequences of making this error?
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