MIE 302 -- Mechanical Engineering Laboratory I
Experiment 1
Statistics of Measurements
(1 week) (revised 12/04)
Objectives: a) To introduce the concept of mean value, x , standard deviation, ,
standard error of the mean,  x , and histogram using measurement of the hardness of a
steel part.
b) To conduct a statistical hypothesis testing to determine whether the
hardness between two steel types are identical.
Equipment: Rockwell hardness tester
Material:
Heat treated drill rod steel
Procedure:
Each group will be given several steel rods (grade W-1 drill rod) with
a square cross-section containing a blind hole. Each student must perform a hardness
test and have a clear understanding of how to operate the Rockwell hardness tester.
There are two categories of rods: Type A and Type B, each type being heat treated
slightly differently from the other. The heat treatment for Type A rod involves
soaking at 850 C for half hour followed by water quenching and then annealing at
200 C for one hour (tempering). Type B rods are tempered at 250 C for one hour
after the high temperature soak and water quench. The task is to make
measurements of the part’s hardness, and then to determine statistically whether the
tempering temperature had an influence on the hardness of the steel.
Before making the hardness measurements, check the calibration of the instrument
using a hardness standard. If the mean value of several measurements on the
standard lies outside the specified range of the standard, correct the data for the part
by the datum error which is the difference of the measured and specified mean
hardness values of the standard.
All measurements should be entered directly into the data book as they are made.
2. Combine the data for hardness with that of other members of the laboratory
session to create a larger data-base for Type A and Type B steels.
3. Make separate histograms for Type A and Type B steel based on group data
alone for the hardness. Complete the histograms during the laboratory period.
6. Calculate the mean value, x , the standard deviation, , and the standard error of
the mean,  x for your group’s data. Draw vertical lines on the histograms
representing x , ( x +  x ), and ( x -  x ).
7. Determine whether the hardness and the part length of the two steel Types are
identical based on your group’s data alone using a Type I error of 5%.
8. Based on the number of samples you tested what magnitude of the difference
between the mean hardness values of A and B can you resolve with a 5% error?
(Hint: Using a type II error of 5% find out the difference between the mean
values for the number of samples you tested using the operating characteristic
curve).
Submit the copy-pages of your data book to your instructor at the end of the
laboratory period.
Pre-Lab:
1) What is hardness and how is it measured? What are different types of
hardness scales? How would you pick which hardness scale to use for a given
material?
2) Write a short report on hypothesis testing. What are Type I and Type II
errors?
Report: A Memorandum Report should have on one page the following:
1. Title, experiment number, author’s name, partners’ name, instructor’s name,
course number, institution, and date
2. Statement of Objectives
3. Brief description of the experiment
4. Statistical analysis of the results along with a clear discussion of what the
results mean.
Allocate about half of the page to items 1 - 3, and the other half to item 4.
Attach to the Memorandum:
1. A Table for x , , and  x for the hardness of Type A and B steel. Contrast
your group’s results with that of the class-combined data.
2. A table showing the equations used for the statistical analysis.
3. Histograms for the hardness for Type A and Type B steel resulting from your
group’s results and from class-pooled data. Each histogram should show the
average, standard deviations and the standard deviations of the mean.
4. A scaled engineering drawing of the part and a schematic drawing of the
hardness tester.
MIE 302 - Mechanical Engineering Laboratory I
Guide for maintaining the Data Book

Write in ink

Start each experiment on a new page.

On the first page of a given experiment show your name as the experimenter, the
number and title of the experiment, the date on which the work was done, and your
lab partners’ names. Only the experiment’s number and title, and the date is needed
for the consecutive pages for the experiment.

State the objective for the experiment.

Show a clear and complete diagram of the apparatus. Label all parts.

Give a list of the equipment and instruments used with make and model numbers.

Prepare a pre-lab approximately 1-3 pages long. You can include figures.

Enter the data in a tabular form only with units as it is being obtained. Do not enter
data onto some piece of paper to be later transferred to the data book.

Give a title to each table.

Draw a box around the data tables. This identifies data from calculated values.

Next to each data table provide a very brief write-up of the procedure you used to
obtain that data.

Don’t leave spaces.

Don’t skip pages.

Data is not erased. If it is incorrect, draw a diagonal line through it with a suitable
explanation.