Engineering Statistics Case Study Solution
Independent sample T-test:
Research Question:
Is there a statistically significant difference between number of suppliers and its three technical machines maintenance costs, which are Standard, DAC and Operator?
Null Hypothesis:
There is no statistically significant difference between number of suppliers and its three technical machines maintenance costs, which are Standard, DAC and Operator.
Alternate Hypothesis:
There is a statistically significant difference between the number of suppliers and their three technical machines maintenance costs, which are Standard, DAC and Operator.
For standard technical machine, p-value is less than 0.05, which provides a strong statistical evidences to reject the null hypothesis ultimately, to accept alternate hypothesis, which tells us that there is a statistical difference between the standard technical machine’s maintenance costs from 4 suppliers.
For DAC technical machine, p-value is less than 0.05, which provides a strong statistical evidences to reject null hypothesis, ultimately to accept alternate hypothesis, which tells that there is a statistically difference between DAC technical machine’s maintenance costs from 4 suppliers.
For Operator technical machine, p-value is greater than 0.05, which does not provide a strong statistical evidences to reject null hypothesis ultimately to reject alternate hypothesis, which tells us that there is a statistically difference between DAC technical machine’s maintenance costs from 4 suppliers.
Independent Chi Square Test:
Research Question:
Is there a statistically significant relationship between the number of suppliers and their three technical machines’ maintenance costs which are Standard, DAC and Operator?
Null Hypothesis:
There is no statistically significant relationship between the number of suppliers and its three technical machines’ maintenance costs, which are Standard, DAC and Operator.
Alternate Hypothesis:
There is a statistically significant relationship between the number of suppliers and their three technical machines maintenance costs, which are Standard, DAC and Operator.
For standard technical machine, p-value is greater than 0.05, which does not provide a strong statistical evidences to reject null hypothesis, which tells that there is a statistically significant relationship between the standard technical machines’ maintenance costs from 4 suppliers.
For DAC technical machine, p-value is greater than 0.05, which does not provide a strong statistical evidences to reject null hypothesis, indicating that there is a statistically significant relationship between the DAC technical machines’ maintenance costs from 4 suppliers.
For Operator technical machine, p-value is greater than 0.05, which does not provide a strong statistical evidences to reject null hypothesis ultimately to reject alternate hypothesis, which tells that there is a statistically significant differences between DAC technical machine’s maintenance costs from 4 suppliers.
Recommendations and Conclusion:
After performing an engineering analysis and a statistical analysis, it has been concluded that the supplier one is capable to meet the project specifications and requirements related to the purchase of three different technical machines,because his average monthly cost of maintenance for three technical machines is less than the other three suppliers.
The total average monthly maintenance for technical machines purchased by supplier one is $ 7,100, which is lesser than the other suppliers’ average monthly maintenance cost for three technical products, which is $ 16,313 for supplier two, $ 13,366 for supplier three and $ 11,889 for supplier four.
Exhibit 1: Regression Analysis
| Model Summary | ||||
| Model | R | R Square | Adjusted R Square | Std. Error of the Estimate |
| 1 | .518 a | .268 | .263 | 2261.7156 |
| a. Predictors: (Constant), Error | ||||
| ANOVA a | ||||||
| Model | Sum of Squares | df | Mean Square | F | Sig. | |
| 1 | Regression | 266602632.395 | 1 | 266602632.395 | 52.118 | .000b |
| Residual | 726380755.542 | 142 | 5115357.433 | |||
| Total | 992983387.938 | 143 | ||||
| a. Dependent Variable: Standrad | ||||||
| b. Predictors: (Constant), Error | ||||||
| Coefficients a | ||||||||
| Model | Unstandardized Coefficients | Standardized Coefficients | t | Sig. | 95.0% Confidence Interval for B | |||
| B | Std. Error | Beta | Lower Bound | Upper Bound | ||||
| 1 | (Constant) | 2306.115 | 306.992 | 7.512 | .000 | 1699.249 | 2912.981 | |
| Error | 46.573 | 6.451 | .518 | 7.219 | .000 | 33.820 | 59.326 | |
| a. Dependent Variable: Standrad | ||||||||
Exhibit 2: Independent Chi Square Test
| Chi-Square Tests | |||
| Value | df | Asymptotic Significance (2-sided) | |
| Pearson Chi-Square | 140.000 a | 135 | .367 |
| Likelihood Ratio | 130.312 | 135 | .598 |
| Linear-by-Linear Association | .008 | 1 | .930 |
| N of Valid Cases | 48 | ||
| a. 184 cells (100.0%) have expected count less than 5. The minimum expected count is .25. | |||
| Symmetric Measures | |||||
| Value | Asymptotic Standardized Error a | Approximate Tb | Approximate Significance | ||
| Interval by Interval | Pearson's R | .013 | .130 | .087 | .931c |
| Ordinal by Ordinal | Spear man Correlation | .074 | .141 | .503 | .617c |
| N of Valid Cases | 48 | ||||
| a. Not assuming the null hypothesis. | |||||
| b. Using the asymptotic standard error assuming the null hypothesis. | |||||
| c. Based on normal approximation. | |||||
Exhibit 3: Percentiles / Quartiles
| Percentiles | |||||||||
| Supplier | Percentiles | ||||||||
| 5 | 10 | 25 | 50 | 75 | 90 | 95 | |||
| Weighted Average(Definition 1) | Standrad | 1 | 1024.000 | 1039.600 | 1372.500 | 2180.000 | 3600.000 | 4227.000 | . |
| 2 | 2100.000 | 2604.000 | 3805.000 | 4180.000 | 8102.500 | 11175.000 | . | ||
| 3 | 730.000 | 1384.000 | 3505.000 | 4175.000 | 5831.250 | 6870.000 | . | ||
| 4 | 1430.000 | 1535.000 | 3802.500 | 4215.000 | 5815.000 | 11226.000 | . | ||
| DAC | 1 | 310.000 | 325.000 | 475.000 | 1105.000 | 1682.500 | 2323.000 | . | |
| 2 | 1670.000 | 2030.000 | 3270.000 | 6500.000 | 6855.000 | 8184.000 | . | ||
| 3 | 530.000 | 587.000 | 1615.000 | 3325.000 | 5662.500 | 11158.000 | . | ||
| 4 | 1700.000 | 1757.000 | 1905.000 | 3300.000 | 4160.000 | 6035.000 | . | ||
| Operator | 1 | 870.000 | 972.000 | 2157.500 | 3315.000 | 4175.000 | 8079.000 | . | |
| 2 | 2760.000 | 2799.000 | 2955.000 | 3830.000 | 6995.000 | 10257.000 | . | ||
| 3 | 530.000 | 608.000 | 1487.500 | 4180.000 | 7805.000 | 9397.000 | . | ||
| 4 | 970.000 | 973.000 | 1207.500 | 4110.000 | 4867.500 | 7930.000 | . | ||
| Tukey's Hinges | Standrad | 1 | 1455.000 | 2180.000 | 3500.000 | ||||
| 2 | 3830.000 | 4180.000 | 7665.000 | ||||||
| 3 | 3590.000 | 4175.000 | 5317.500 | ||||||
| 4 | 3805.000 | 4215.000 | 5480.000 | ||||||
| DAC | 1 | 480.000 | 1105.000 | 1645.000 | |||||
| 2 | 3330.000 | 6500.000 | 6820.000 | ||||||
| 3 | 2110.000 | 3325.000 | 5205.000 | ||||||
| 4 | 1910.000 | 3300.000 | 4020.000 | ||||||
| Operator | 1 | 2205.000 | 3315.000 | 4120.000 | |||||
| 2 | 3010.000 | 3830.000 | 6650.000 | ||||||
| 3 | 2145.000 | 4180.000 | 7490.000 | ||||||
| 4 | 1215.000 | 4110.000 | 4845.000 | ||||||
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