Pilgrim Bank (A): Customer Profitability Case Study Solution
The output summary of the two sample t-test of data shows that the mean of the age with missing values and without missing values are 3.98 and 4.038, respectively. Additionally, in the 95 percent confidence interval two sample t-test; the p value is 0.12, which is greater than the significance level of 0.05, hence providing strong statistical evidence for the null hypothesis, stating that there is not any difference in the mean value of age with missing value and without missing value. Furthermore;the t value is -1.53, which is less than the value of 1.96, hence providing statistical evidences that the value is not statistically significant.
Income
The hypothesis of evaluating the difference in the data of income with missing values and without missing values, are generated below:
H0 = There is not any significant difference in the data of income with missing values and without the missing values.
H1 = There is a significant difference in the data of income with missing values and without the missing values
The output summary of the two sample t-test of data shows that the mean of the income with missing values and without the missing values are:5.45 and 5.34,respectively. Additionally, in the 95 percent confidence interval two sample t-test; the p value is 0.00, which is lower than the significance level of 0.05, hence providing strong statistical evidence of rejecting the null hypothesis which states there is no difference in the mean value of income with missing value and without the missing value. Furthermore, the t value is 5.55, which is greater than the value of 1.96, hence providing statistical evidence that the value is a statistically significant.
Combining the analysis of the aforementioned variables data; it is analyzed that there is not any significant difference in the data of age, with and without the missing values. At the same time; the analysis of the data of income, with and without missing values, shows that there is a significant difference in the data of income, with and without the missing values.
Profit
The hypothesis of evaluating the difference in the data of profits with missing values and without missing values, are generated below:
H0 = There is not any significant difference in the data of profits with missing values and without the missing values.
H1 = There is a significant difference in the data of profits with the missing values and without the missing values
The output summary of the two sample t-test of data shows that the mean of the income with and without missing values are: 144.82 and 111.50, respectively. Additionally, in the 95 percent confidence interval two sample t-test; the p value is 0.00, which is lower than the significance level of 0.05, hence providing strong statistical evidence of rejecting the null hypothesis that there is no difference in the mean value of profit, with or without the missing values.
Question 3 - Newly constructed test
Taking under consideration the analysis;the non-valuable customers and valuable customers are differentiated based on the average of profitability. It is assumed that if the profitability of the online customers is below the average of the total profit levels; the customers are considered to be non-valuable.Whereas, if the profitability of the online customers is above average of the total profit levels; the customers are considered to be valuable. Thus, the total valuable and non-valuable online customers of the bank are:1269 and 2585, respectively. Additionally, the output summary of the total sample t test shows that the mean of the value of customer profit and the non-valuable customer profit are: 414.79 and -29.68,respectively. Additionally, in the 95 percent confidence interval two sample t-test; the p value is 0.00, which is lower than the significance level of 0.05, hence providing a strong statistical evidence of rejecting the null hypothesis that there is not any difference in the online and valuable customers. Hence, it is to conclude that moving online makes customers more valuable due to which the company must accelerate its efforts in online selling to achieve higher returns in the near future.
Appendix A –Missing and non-missing values data
| Age | ||
| t-Test: Two-Sample Assuming Unequal Variances | ||
| Variable 1 | Variable 2 | |
| Mean | 3.9886846 | 4.038345 |
| Variance | 2.7023834 | 3.0352 |
| Observations | 2828 | 31634 |
| Hypothesized Mean Difference | 0 | |
| df | 3420 | |
| t Stat | -1.531434 | |
| P(T<=t) one-tail | 0.0628773 | |
| t Critical one-tail | 1.6452993 | |
| P(T<=t) two-tail | 0.1257547 | |
| t Critical two-tail | 1.9606579 | |
| Income | ||
| t-Test: Two-Sample Assuming Unequal Variances | ||
| Variable 1 | Variable 2 | |
| Mean | 5.4587772 | 5.344692 |
| Variance | 5.5078526 | 5.87347 |
| Observations | 23373 | 31634 |
| Hypothesized Mean Difference | 0 | |
| df | 51218 | |
| t Stat | 5.5580428 | |
| P(T<=t) one-tail | 1.371E-08 | |
| t Critical one-tail | 1.6448834 | |
| P(T<=t) two-tail | 0.000000 | |
| t Critical two-tail | 1.9600103 | |
| Profit | ||
| t-Test: Two-Sample Assuming Unequal Variances | ||
| Variable 1 | Variable 2 | |
| Mean | 111.50269 | 144.827 |
| Variance | 74441.334 | 152095.9 |
| Observations | 31634 | 26396 |
| Hypothesized Mean Difference | 0 | |
| df | 45960 | |
| t Stat | -11.69794 | |
| P(T<=t) one-tail | 7.238E-32 | |
| t Critical one-tail | 1.6448868 | |
| P(T<=t) two-tail | 0.00 | |
| t Critical two-tail | 1.9600156 |
Appendix B – Demographics & online/offline
| Regression Statistics | |
| Multiple R | 0.223004 |
| R Square | 0.049731 |
| Adjusted R Square | 0.049611 |
| Standard Error | 265.9854 |
| Observations | 31634 |
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | -71.922 | 37.94073 | -1.89564 | 0.058017 | -146.287 | 2.443317 | -146.287 | 2.443317 |
| X Variable 1 | 9.300115 | 0.901253 | 10.31909 | 0.00000 | 7.533624 | 11.06661 | 7.533624 | 11.06661 |
| X Variable 2 | 11.65493 | 0.619017 | 18.82812 | 0.00000 | 10.44163 | 12.86823 | 10.44163 | 12.86823 |
| X Variable 3 | 5.448961 | 0.18569 | 29.34434 | 0.00000 | 5.085 | 5.812921 | 5.085 | 5.812921 |
| X Variable 4 | 0.023437 | 0.03123 | 0.750484 | 0.452969 | -0.03777 | 0.084649 | -0.03777 | 0.084649 |
Appendix C – New model
| t-Test: Two-Sample Assuming Unequal Variances | ||
| Variable 1 | Variable 2 | |
| Mean | 414.7911742 | -29.6851 |
| Variance | 102500.8041 | 4608.696 |
| Observations | 1269 | 2585 |
| Hypothesized Mean Difference | 0 | |
| df | 1324 | |
| t Stat | 48.91870026 | |
| P(T<=t) one-tail | 2.2629E-299 | |
| t Critical one-tail | 1.646005321 | |
| P(T<=t) two-tail | 0.00000 | |
| t Critical two-tail | 1.961757341 |
..............
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