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. 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.

2. 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.

3. 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?

Machine 1: count =105, mean= 3.49484, std dev= .0482031 confidence interval ( 3.488551 to 3.50417) p value<.0001

Machine 2: count= 102, mean 3.52563, std dev= .0581058, confidence interval (3.51422 to 3.53705) p-value<.0001

Machine 3: count = 100 mean 3.52883, std dev= .083338 confidence interval ( 3.51229 to 3.54536) P Vale<.0001