Download MM_Lab

ISE 482L – Lab I
M&M Experiment
Statistical and Quality Control
Experimental Application
ISE 482L: Lab I
Purpose:
The purpose of the following experiment is to determine through Probability and Statistics weather the
actual M&M color percentages per bag are significantly different and to determine if the process of
producing these bags of M&M’s is in control.
Equipment/ Materials:
M&M bag (2)
Minitab
Caliper
Microsoft EXCEL
Procedure:
Part A
1. Open the M&M bag.
2. Count the total number of M&M’s in the bag and record the number in the table below.
Bag
1
2
2.
Number of M&M’s
Keep each bag separate from each other. (Include broken or misshaped M&M’s)
3. Separate the M&M’s into groups of 6, with each group containing one of every color.
4. Once separated into groups, you can now eat any leftover M&M’s.
5. Now measure the diameter of each M&M in every group and record it in the table using
Microsoft Excel. Then repeat steps 1-4 for Bag 2.
6. Now create control charts, the R chart and X-bar chart, from the data collected above using
Excel. (Remember to include all calculations such as X-bar bar, the UCL, and the LCL.)
7. Using your knowledge of quality apply the 8 rules to see if any are being violated within your
data set. Record your findings in a table.
ISE 482L: Lab I
Part B
1. Using the diameter data gathered in Part A, test to see if the mean diameter of Bag 1 is
equal to 0.500 inches using Minitab. Record statistical test information and conclusion on an
attached statistical template.
2. Repeat step 1 for Bag 2; however, this time test to see if the mean diameter is greater than
0.525 inches using Minitab. Record statistical test information and conclusion on an
attached statistical template.
3. Now, test to see if the mean diameters of Bag 1 and Bag 2 are equal. Record statistical test
information and conclusion on an attached statistical template.
Report:
1. Purpose
2. Procedure
3. Results
a. Include all tables and graphs.
4. Conclusions
a. Discuss if the process is in control.
b. Discuss reasons for process being out of control or in control.
c. Discuss the meaning of the statistical test findings.
ISE 482L: Lab I
Typical Hypothesis Test Template
Problem Statement:
Hypotheses:
H0:
H1:
Critical values for determining correct test statistic:
Calculation of test statistic and p-value:
(Computer Output)
Graphics: (Choose applicable graphic drawn by hand or computer)
Gamma Probability Density Function
t Distribution
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
Standard Score (t)
0
0.05
3.0
4.0
0.0
2.0
1
4.0
6.0
8.0
10.0
(p-value)
Decision:
_________H0
Conclusion:
Use complete sentences. (Refer to problem statement and managerial decision based on p-values
ISE 482L: Lab I
Examples of Completed Lab
Single sample hypothesis test
Hypotheses:
H0:
 = .5
H1:
 ≠ .5
Critical values: *small sample
*sigma unknown
*two-sided alternate hypothesis
*p-value approach
Calculation of test statistic and p-value:
One-Sample T: Bag 1
Test of mu = 0.5 vs not = 0.5
Variable
Bag 1
N
Mean
StDev
SE Mean
95% CI
60
0.52368
0.00938
0.00121
(0.52126, 0.52611)
T
P
19.56
0.000
Graphics:
t Distribution
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
Standard Score (t)
or
0
0.05
1 p-value
Decision:
Reject H0
Conclusion:
inches.
With a p-value = 0.00016, the data suggest that the mean diameter for Bag 1 is not equal 0.5
ISE 482L: Lab I
Single sample hypothesis test
Hypotheses:
H0:
 = .525
H1:
 > .525
Critical values: *small sample
*sigma unknown
*one-sided alternate hypothesis
*p-value approach Therefore, there is no value for t critical
Calculation of test statistic and p-value:
One-Sample T: Bag 1
One-Sample T: Bag 2
Test of mu = 0.525 vs > 0.525
Variable
Bag 2
N
58
Mean
0.52662
StDev
0.00969
SE Mean
0.00127
95% Lower
Bound
0.52449
T
1.27
P
0.104
Graphics:
t Distribution
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
Standard Score (t)
or
0
Decision:
0.05
1 p-value
Fail to Reject H0
Conclusion:
With a p-value = 0.104, the data suggest that mean diameter of Bag 2 is not a significant
statistical greater than 0.525 inches.
ISE 482L: Lab I
Two sample hypothesis test
Hypotheses:
H0:
1 = 2
H1:
1 ≠ 2
Critical values: *small sample
*sigma unknown
*one-sided alternate hypothesis
*p-value approach
Calculation of test statistic and p-value:
Two-Sample T-Test and CI: Bag 1, Bag 2
Two-sample T for Bag 1 vs Bag 2
Bag 1
Bag 2
N
60
58
Mean
0.52368
0.52662
StDev
0.00938
0.00969
SE Mean
0.0012
0.0013
Difference = mu (Bag 1) - mu (Bag 2)
Estimate for difference: -0.00294
95% CI for difference: (-0.00642, 0.00054)
T-Test of difference = 0 (vs not =): T-Value = -1.67
P-Value = 0.097
DF = 115
Graphics:
t Distribution
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
3.0
4.0
Standard Score (t)
or
0
Decision:
0.05
1 p-value
Fail to Reject H0
Conclusion:
With a p-value = 0.097, the data suggest that mean diameter of Bag 1 is not a significant
statistical different than the mean of Bag 2.