Project #2 MATH 153 / BUS 240 Business Topic: Quality Control 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 means 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. Project #2Grading Rubric Grade Component Description Grade Weight Comparative Graphs #1 Student shows an understanding of data analysis by providing all useful graphs for analyzing the data. Graphs are made with technology (Fathom) and are adjusted as necessary so that they do a good job of displaying the distributions. 10% All Steps Shown for Inference Procedures for #2 Student performs all steps in the inference procedure(s): see “Wrap-Up” for Topic 17 p.368-369, and “Step 6” on page 359 that was missed in the “Wrap-Up”, and see the six steps again for means on page 425. Fathom or other technology should be used to calculate confidence intervals, and for the test stats & p-values of significance tests. 30% All Steps Shown for Inference Procedures for #3 Student performs all steps in the inference procedure(s): see “Wrap-Up” for Topic 17 p.368-369, and “Step 6” on page 359 that was missed in the “Wrap-Up”, and see the six steps again for means on page 425. Fathom or other technology should be used to calculate confidence intervals, and for the test stats & p-values of significance tests. 30% Business Decisions (conclusions) in Context Student writes a well-written statement of the conclusions for the inference procedure(s) for each machine. Conclusions are supported with appropriate calculations from the inference procedures. Conclusions are not generic, but rather specifically state what should be done with each machine. 20% All Steps Shown for Inference Procedures for #4 Student performs all steps in the inference procedures. Conclusion about the employee’s honesty reasonably follows from the results of the significance tests. 10% Connections Student performs both types of inference procedures (interval & test) in each situation for each machine, showing strong knowledge of how these procedures are “duals” of each other, and how their different perspectives show the same conclusion. up to 10%
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