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 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.