By,     Quality                   ANIL KUMAR SAHU - 20104004Associates, Inc.               SANDEEP PRASAD - 20104005      ...
Coverage                 Case Understanding -                       Case Analysis -       Beyond Case Analysis - Sarjeevan...
Case facts• Quality Associates       ~ Client (Mfg. Company)    (Consulting Firm)• Initial Client Sample : 800 observation...
Given Data:                    n             = 30                    µ             = 12                    No. of samples ...
Analysis                                Sample 2                     Sample 18                      7                     ...
Analysis                                                Box Plot9876543210    10             10.5         11      11.5    ...
Analysis                  CO-VARIANCE           SAMPLE 1    SAMPLE 2            SAMPLE 3    SAMPLE 4SAMPLE 1    0.046938SA...
Analysis                CO-RELATION           SAMPLE 1         SAMPLE 2              SAMPLE 3       SAMPLE 4SAMPLE 1      ...
Analysis                       Descriptive statistics : Summary TableSAMPLE 1                 SAMPLE 2                    ...
Analysissample size              DataPopulation Standard Deviation                     0.21Sampling Error                 ...
Analysissample size             30.00          30.00         30.00   30.00sample mean             11.96          12.03    ...
Sample 1                                                      Sample 2                          P=.028                    ...
Analysisa) Result       Do not Reject H0 Do not Reject H0        Reject H0   Do not Reject H0b) std. dev.          0.22   ...
Conclusion• More samples are required in order to determine  variability in the process.• The samples can be collected at ...
Sarjeevan Sainbhi   15
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Q2 exe mba10-qm_quality associates_20104004-05-06

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Q2 exe mba10-qm_quality associates_20104004-05-06

  1. 1. By, Quality ANIL KUMAR SAHU - 20104004Associates, Inc. SANDEEP PRASAD - 20104005 SARJEEVAN SAINBHI - 20104006SCHOOL OF PETROLEUM MANAGEMENT, PDPU. Quantitative Methods Sarjeevan Sainbhi 1
  2. 2. Coverage Case Understanding - Case Analysis - Beyond Case Analysis - Sarjeevan Sainbhi 2
  3. 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”. Sarjeevan Sainbhi 3
  4. 4. Given Data: n = 30 µ = 12 No. of samples = 4 σ = 0.21 S = 0.21Sarjeevan Sainbhi 4
  5. 5. Analysis Sample 2 Sample 18 7 8 6 66 5 6 4 4 4 4 3 34 3 3 3 2 2 2 2 1 1 0 0 02 1 0 0 0 00 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. 6. Analysis Box Plot9876543210 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 Sarjeevan Sainbhi 6
  7. 7. Analysis CO-VARIANCE SAMPLE 1 SAMPLE 2 SAMPLE 3 SAMPLE 4SAMPLE 1 0.046938SAMPLE 2 0.046938 0.046938SAMPLE 3 0.008929 0.008929 0.041489SAMPLE 4 0.009392 0.009392 0.013891 0.041065 Sarjeevan Sainbhi 7
  8. 8. Analysis CO-RELATION SAMPLE 1 SAMPLE 2 SAMPLE 3 SAMPLE 4SAMPLE 1 1SAMPLE 2 1 1SAMPLE 3 0.202328 0.202328 1SAMPLE 4 0.213919 0.213919 0.336544 1 Sarjeevan Sainbhi 8
  9. 9. Analysis Descriptive statistics : Summary TableSAMPLE 1 SAMPLE 2 SAMPLE 3 SAMPLE 4 Mean 11.9587 Mean 12.0287 Mean 11.8890 Mean 12.0813Standard Error 0.0402 Standard Error 0.0402 Standard Error 0.0378 Standard Error 0.0376Median 11.9550 Median 12.0250 Median 11.9200 Median 12.0800 Mode 11.9300 Mode 12.0000 Mode 11.9500 Mode 12.0200Standard Standard Standard StandardDeviation 0.2204 Deviation 0.2204 Deviation 0.2072 Deviation 0.2061 Sample Sample SampleVariance 0.0486 Variance 0.0486 Sample Variance 0.0429 Variance 0.0425Skewness -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 Sarjeevan Sainbhi 9
  10. 10. Analysissample size DataPopulation Standard Deviation 0.21Sampling Error 0.04Confidence Level 99% Intermediate CalculationsZ Value -2.5758293Calculated Sample Size 182.8743376 ResultSample Size Needed 183 Finite PopulationsPopulation Size 800Sample Size with FPC 149.0001973Sample Size Needed Sarjeevan Sainbhi 150 10
  11. 11. Analysissample size 30.00 30.00 30.00 30.00sample mean 11.96 12.03 11.89 12.08population std. dev. 0.21 0.21 0.21 0.21co-efficient of 1.84% 1.83% 1.74% 1.71%variationhypothesis value 12.00 12.00 12.00 12.00standard error 0.04 0.04 0.04 0.04test statistic z = -1.08 0.75 -2.90 2.12p- value (lower tail) 0.14 0.77 0.002 0.98P-value (upper-tail) 0.86 0.23 1.00 0.02p - value (two tail) 0.28 0.45 0.004 0.03α 0.01 0.01 0.01 0.01α/2 0.005 0.005 0.005 0.005 Sarjeevan Sainbhi 11
  12. 12. Sample 1 Sample 2 P=.028 P=.45 P=.028 P=.45α=.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=.005P=.004 P=.004 -2.12 2.12 -2.90 2.90 -2.576 Sarjeevan Sainbhi -2.576 2.576 12 2.576
  13. 13. Analysisa) Result Do not Reject H0 Do not Reject H0 Reject H0 Do not Reject H0b) 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 12.19M.E. Lower limit =sample mean - 11.85 11.92 11.78 11.97M.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 Limitd) Changing α Sarjeevan Sainbhi 13
  14. 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. Sarjeevan Sainbhi 14
  15. 15. Sarjeevan Sainbhi 15

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