# Quality control calculus for business,

A quality control supervisor is looking at production machines used to fabricate steel pins for a particular product assembly. The desired specifications for acceptable pins is for a diameter of 3.52 mm, with acceptable pins being within +/- 0.1 mm. The machine must be realigned to the target diameter if it appears that the population mean for all rods produced by that machine is different than 3.52 mm at 95% confidence/5% significance. A machine must be recalibrated for consistency if it appears that the population percentage (proportion) of unacceptable rods is above 10%, again at 95% confidence/5% significance. The accompanying Fathom file contains rod diameter measurements in mm for random samples of rods taken from three different production machines on a given day. The goal of this project is for you to apply statistical inference procedures (confidence intervals and significance tests) to determine which if any of the machines need to be serviced, and how. 1. Produce appropriate graphs to display the sample distributions, and briefly comment on what they reveal or don’t reveal. 2. Conduct appropriate inference procedure(s) for each machine to determine if the population mean rod diameter for rods produced by that machine appears to be 3.52 mm, using 95% confidence/5% significance. Make sure you complete all of the steps for the procedure, including a check of the technical conditions. Fathom or other technology should be used, rather than by-hand calculations. Make sure to state your conclusions in context, indicating whether or not each machine should be serviced to realign the target diameter. 3. Conduct appropriate inference procedure(s) for each machine to determine if the population proportion of unacceptable rods produced by that machine appears to be more than 0.10, using 95% confidence/5% significance. Make sure you complete all of the steps for the procedure, including a check of the technical conditions. Fathom or other technology should be used, rather than by-hand calculations. Make sure to state your conclusions in context, indicating whether or not each machine should be serviced to recalibrate for consistency. While looking at a graph, you can right-click on the center of a graph and choose “Plot Value” to graph a vertical line at each of the cutoffs for acceptable rods, 3.42 and 3.62, in order to see which rods fall outside the acceptable range. Also, items are dynamically linked in Fathom, so if you click on a point on the graph, or select a group of points by click-holding and drawing a box around them, the point(s) are highlighted on any comparative graphs and their row(s) in the table are highlighted as well. The video here shows how this can be done. http://screencast.com/t/Fvtct098 4. An employee claims that random samples were not in fact taken from both Machine 2 and Machine 3, but rather both samples were taken from the same machine. Perform significance  tests to compare the population mean rod diameters, and population proportions of unacceptable rods using the samples “supposedly” from Machine 2 and Machine 3. Using support from the results of these procedures, do you think that the employee is telling the truth? Your submission should be typed in a word processor, and saved as .doc, .docx, or .pdf format. The graphs and Fathom Summary calculation boxes must be included. Make sure all calculations are interpreted in context, and that you explain what they mean in answering the questions.   A quality control supervisor is looking at production machines used to fabricate steel pins for a particular product assembly. The desired specifications for acceptable pins is for a diameter of 3.52 mm, with acceptable pins being within +/- 0.1 mm. The machine must be realigned to the target diameter if it appears that the population mean for all rods produced by that machine is different than 3.52 mm at 95% confidence/5% significance. A machine must be recalibrated for consistency if it appears that the population percentage (proportion) of unacceptable rods is above 10%, again at 95% confidence/5% significance. The accompanying Fathom file contains rod diameter measurements in mm for random samples of rods taken from three different production machines on a given day. The goal of this project is for you to apply statistical inference procedures (confidence intervals and significance tests) to determine which if any of the machines need to be serviced, and how. 1. Produce appropriate graphs to display the sample distributions, and briefly comment on what they reveal or don’t reveal. 2. Conduct appropriate inference procedure(s) for each machine to determine if the population mean rod diameter for rods produced by that machine appears to be 3.52 mm, using 95% confidence/5% significance. Make sure you complete all of the steps for the procedure, including a check of the technical conditions. Fathom or other technology should be used, rather than by-hand calculations. Make sure to state your conclusions in context, indicating whether or not each machine should be serviced to realign the target diameter. 3. Conduct appropriate inference procedure(s) for each machine to determine if the population proportion of unacceptable rods produced by that machine appears to be more than 0.10, using 95% confidence/5% significance. Make sure you complete all of the steps for the procedure, including a check of the technical conditions. Fathom or other technology should be used, rather than by-hand calculations. Make sure to state your conclusions in context, indicating whether or not each machine should be serviced to recalibrate for consistency. While looking at a graph, you can right-click on the center of a graph and choose “Plot Value” to graph a vertical line at each of the cutoffs for acceptable rods, 3.42 and 3.62, in order to see which rods fall outside the acceptable range. Also, items are dynamically linked in Fathom, so if you click on a point on the graph, or select a group of points by click-holding and drawing a box around them, the point(s) are highlighted on any comparative graphs and their row(s) in the table are highlighted as well. The video here shows how this can be done. http://screencast.com/t/Fvtct098 4. An employee claims that random samples were not in fact taken from both Machine 2 and Machine 3, but rather both samples were taken from the same machine. Perform significance  tests to compare the population mean rod diameters, and population proportions of unacceptable rods using the samples “supposedly” from Machine 2 and Machine 3. Using support from the results of these procedures, do you think that the employee is telling the truth? Your submission should be typed in a word processor, and saved as .doc, .docx, or .pdf format. The graphs and Fathom Summary calculation boxes must be included. Make sure all calculations are interpreted in context, and that you explain what they mean in answering the questions.

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