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Over a long period of time, the production of 1000 high-quality hammers in a factory seems to have reached a weight with an average of 884? and standard deviation of 41.9?. Propose a model for the weight of the hammers including a probability distribution for the weight. Provide all the assumptions needed for this model to hold (even the uncertain ones)? What parameters does this model have? One aims at answering the following questions about a new production system: • Does the new system make more constant weights? • Does the new system make lower weights? • Does the new system make higher weights? • Does the new system make less constant weights? To answer this question a random sample of newly produced hammers is evaluated yielding the weights 959, 824, 795, 811, 895, 987, 744, 914, 807, 786.  What hypotheses can you propose to test the question? What test and decision rule can you make to estimate if the new system answers the given question? Express the decision rules as logical statements involving critical values. What error probabilities can you suggest and why? Perform the test and draw the conclusion to answer the question.

Over a long period of time, the production of 1000 high-quality hammers in a factory seems to have reached a weight with an average of 884? and standard deviation of 41.9?. Propose a model for the weight of the hammers including a probability distribution for the weight. Provide all the assumptions needed for this model to hold (even the uncertain ones)? What parameters does this model have? One aims at answering the following questions about a new production system: • Does the new system make more constant weights? • Does the new system make lower weights? • Does the new system make higher weights? • Does the new system make less constant weights? To answer this question a random sample of newly produced hammers is evaluated yielding the weights 959, 824, 795, 811, 895, 987, 744, 914, 807, 786.  What hypotheses can you propose to test the question? What test and decision rule can you make to estimate if the new system answers the given question? Express the decision rules as logical statements involving critical values. What error probabilities can you suggest and why? Perform the test and draw the conclusion to answer the question.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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Over a long period of time, the production of 1000 high-quality hammers in a factory seems to have reached a weight with an average of 884? and standard deviation of 41.9?. Propose a model for the weight of the hammers including a probability distribution for the weight. Provide all the assumptions needed for this model to hold (even the uncertain ones)? What parameters does this model have?


One aims at answering the following questions about a new production system:
• Does the new system make more constant weights?
• Does the new system make lower weights?
• Does the new system make higher weights?
• Does the new system make less constant weights?


To answer this question a random sample of newly produced hammers is evaluated yielding the weights 959, 824, 795, 811, 895, 987, 744, 914, 807, 786. 
What hypotheses can you propose to test the question? What test and decision rule can you make to estimate if the new system answers the given question? Express the decision rules as logical statements involving critical values. What error probabilities can you suggest and why? Perform the test and draw the conclusion to answer the question.

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