Pilgrim Bank (A): Customer Profitability Harvard Case Solution & Analysis

Pilgrim Bank (A): Customer Profitability Case Study Solution

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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