This document analyzes data from samples taken of a manufacturing process to determine if it is operating satisfactorily. It summarizes the sample sizes, means, and standard deviations. Hypothesis tests are run and none of the samples show evidence to reject the null hypothesis that the mean is 12. While more samples may be needed to better understand variability, the analysis shows the process means are within limits and no corrective action is currently required. Changing the significance level could result in rejecting the null hypothesis for some samples.

1. By,
Quality ANIL KUMAR SAHU - 20104004
Associates, Inc. SANDEEP PRASAD - 20104005
SARJEEVAN SAINBHI - 20104006
SCHOOL OF PETROLEUM MANAGEMENT, PDPU.
Quantitative Methods
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2. Coverage
Case Understanding -
Case Analysis -
Beyond Case Analysis -
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3. Case facts
• Quality Associates ~ Client (Mfg. Company)
(Consulting Firm)
• Initial Client Sample : 800 observation
• Quality Associates Suggestion : Random sample
of 30 to monitor the process.
• Hypothesis
H0 : µ = 12 ; Ha : µ ≠ 12
• Requirement:
“If the process was not operating Satisfactorily,
corrective actions could be taken”.
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4. Given Data:
n = 30
µ = 12
No. of samples = 4
σ = 0.21
S = 0.21
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5. Analysis Sample 2
Sample 1
8 7 8 6 6
6 5 6 4 4
4 4 3 3
4 3 3 3 2
2 2 2 1 1
0 0 0
2 1 0
0 0 0
0
11.9
12
More
11.5
11.6
11.7
11.8
12.1
12.2
12.3
12.4
12.5
11.5 11.7 11.9 12.1 12.3 12.5
Frequency Frequency
10 8
10 9 6
4 4 4 5 4
5 3 3
2 2
1 2 2 2 2
0 0 0 0 0
1 1
0
0 0
Frequency Frequency
Sample 3 Sarjeevan Sainbhi
Sample 4 5

6. Analysis
Box Plot
9
8
7
6
5
4
3
2
1
0
10 10.5 11 11.5 12 12.5 13 13.5 14
Series1 Series2 Series3 Series4 Series5 Series6 Series7
Series8 Series9 Series10 Series11 Series12 Series13 Series14
Series15 Series16 Series17 Series18 Series19 Series20 Series21
Series22 Series23 Series24 Series25 Series26 Series27 Series28
Series29 Series30 Series31 Series32
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7. Analysis
CO-VARIANCE
SAMPLE 1 SAMPLE 2 SAMPLE 3 SAMPLE 4
SAMPLE 1 0.046938
SAMPLE 2 0.046938 0.046938
SAMPLE 3 0.008929 0.008929 0.041489
SAMPLE 4 0.009392 0.009392 0.013891 0.041065
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8. Analysis
CO-RELATION
SAMPLE 1 SAMPLE 2 SAMPLE 3 SAMPLE 4
SAMPLE 1 1
SAMPLE 2 1 1
SAMPLE 3 0.202328 0.202328 1
SAMPLE 4 0.213919 0.213919 0.336544 1
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9. Analysis
Descriptive statistics : Summary Table
SAMPLE 1 SAMPLE 2 SAMPLE 3 SAMPLE 4
Mean 11.9587 Mean 12.0287 Mean 11.8890 Mean 12.0813
Standard
Error 0.0402 Standard Error 0.0402 Standard Error 0.0378 Standard Error 0.0376
Median 11.9550 Median 12.0250 Median 11.9200 Median 12.0800
Mode 11.9300 Mode 12.0000 Mode 11.9500 Mode 12.0200
Standard Standard Standard Standard
Deviation 0.2204 Deviation 0.2204 Deviation 0.2072 Deviation 0.2061
Sample Sample Sample
Variance 0.0486 Variance 0.0486 Sample Variance 0.0429 Variance 0.0425
Skewness -0.2350 Skewness -0.2350 Skewness -0.5225 Skewness -0.3896
Sum 358.7600 Sum 360.8600 Sum 356.6700 Sum 362.4400
Count 30.0000 Count 30.0000 Count 30.0000 Count 30.0000
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10. Analysis
sample size
Data
Population Standard Deviation 0.21
Sampling Error 0.04
Confidence Level 99%
Intermediate Calculations
Z Value -2.5758293
Calculated Sample Size 182.8743376
Result
Sample Size Needed 183
Finite Populations
Population Size 800
Sample Size with FPC 149.0001973
Sample Size Needed Sarjeevan Sainbhi 150 10

11. Analysis
sample size 30.00 30.00 30.00 30.00
sample mean 11.96 12.03 11.89 12.08
population std. dev. 0.21 0.21 0.21 0.21
co-efficient of
1.84% 1.83% 1.74% 1.71%
variation
hypothesis value 12.00 12.00 12.00 12.00
standard error 0.04 0.04 0.04 0.04
test statistic z = -1.08 0.75 -2.90 2.12
p- value (lower tail) 0.14 0.77 0.002 0.98
P-value (upper-tail) 0.86 0.23 1.00 0.02
p - value (two tail) 0.28 0.45 0.004 0.03
α 0.01 0.01 0.01 0.01
α/2 0.005 0.005 0.005 0.005
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12. Sample 1 Sample 2
P=.028 P=.45
P=.028 P=.45
α=.005 α=.005 α=.005 α=.005
-1.08 1.08 -0.75 0.75
-2.576 2.576 -2.576 2.576
Sample 3 Sample 4
P=.03
P=.03
α=.005 α=.005 α=.005 α=.005
P=.004
P=.004
-2.12 2.12
-2.90 2.90
-2.576 Sarjeevan Sainbhi -2.576 2.576 12
2.576

13. Analysis
a) Result Do not Reject H0 Do not Reject H0 Reject H0 Do not Reject H0
b) std. dev. 0.22 0.22 0.21 0.21
M.E. 0.11 0.11 0.11 0.11
Upper limit =
sample mean + 12.07 12.14 12.00 12.19
M.E.
Lower limit =
sample mean - 11.85 11.92 11.78 11.97
M.E.
c) Interval Do not Reject H0: Do not Reject H0: Do not Reject H0: Do not Reject H0:
Estimate within Limit within Limit within Limit within Limit
d) Changing α
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14. Conclusion
• More samples are required in order to determine
variability in the process.
• The samples can be collected at different time &
days of operation to monitor the process
effectively.
• The sample standard deviation varies within the
sample.
• As all the Same Mean are within limited thus No
corrective action is required.
• As the value of α is changed to larger value, the P
value reduces leading to rejection of Null
hypothesis.
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15. Sarjeevan Sainbhi 15