Quality control Calculus for Business,
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 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 dont 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 employees 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.
