**Pilgrim Bank (A): Customer Profitability Case Solution **

### Executive summary

The paper sets out to explore the managerial decision making which is critically informed by the analysis of data. In the retail bank, the decision making relates to the policy of the bank towards the online banking. The management team of the bank is concerned about evaluating whether the bank need to charge for the access to the online banking, offer incentives for using the services or devise some other policy altogether. With huge number of customers already using the online site, the bank is well positioned to evaluate the effect of the banking services on the retention and profitability of the customer before making final policy decisions. The total number of customers of the bank are 31634 out of which 3854 are the online customers and 27780 are the offline customers. The ANOVA summary shows that the p value is 0.2098 which is significantly greater than the significance value of 0.05, thus providing a strong evidence of rejecting the alternate hypothesis which states that there is a significant difference between online and offline customers.

### Case Dilemma

Pilgrim Bank is one of the leading and valuable financial institution, which is confronted with an issue of evaluating and assessing the internet strategy’s effectiveness. Additionally, the company is concerned regarding whether should it start charging fees for online banking channel usage or should it start offering customer incentives, such as: lower service charges or rebates to encourage the greater use of the channel.Also, the management must determine the difference between the profitability of offline and online customers.

### Meaningful difference in the profitability of online customers vs. offline customers

The total number of the bank’s customers are 31634, out of which 3854 are the online customers and 27780 are the offline customers. Regardless of the types of customers; the hypothesis is generated, which are as follows:

H0 = There is not a significance difference between the online and offline customers.

H1 = There is a significance difference between the online and offline customers.

The mean profitability level of online customers and offline customers are116.66 and 110.78, respectively. Additionally, in the 95 percent confidence interval; two sample t-test, the p value is 0.22, which is greater than the significance level of 0.05 and the t value is -1.21, which is less than the value of 1.96, hence providing the statistical evidence that the value is not statistically significant. Due to this, we have failed to reject the null hypothesis, which states that there is not any significance difference between the online and offline customers. Moreover, the standard deviation of profitability of both types of customers is 273 and the average profitability of each type of customer is 111, which means that the difference is not huge between the online and offline customers of the company.

The regression analysis is performed with the use of the profitability levels as a dependent variable and the online/offline as the independent variable. The output summary of the regression analysis shows that the R square is 0.000050, which means that the regression model is 0.0050% fitted to the observed data. Furthermore, the multiple R square value is 0.0070, which means that 0.705% is the variance in the dependent variable (profit levels of the bank) that could be explained by the predictor variables (offline/online).

In addition to this; the ANOVA summary shows that the p value is 0.2098, which is significantly greater than the significance value of 0.05, thus providing a strong evidence of rejecting the alternate hypothesis which states that there is a significant difference between the online and offline customers.

In addition to this, the role of customer demographics in comparing the offline and online profitability, is also evaluated using the regression model.

H0 = There is not any significant impact of the role of demographics over the offline as well as online profitability

H1 =There is a significant impact of the role of demographics over the offline as well as the online profitability

In the regression model;the output summary shows that the R square is 0.049, which means that the regression model is 4.97% fitted to the observed data. Furthermore, the multiple R square value is 0.223, which means that 22.30 % is the variance in the dependent variable (offline & online profitability) that could be explained by the predictor variables (district, age, tenure and income).

In addition to this; the ANOVA summary shows that the p value is 0, which is significantly lower than the significance value of 0.05, thus providing a strong evidence of rejecting the null hypothesis which states that there is not any significant difference between the profitability of the bank and other variables including: district, age, tenure and income.

The missing values in the provided data is filled using the RANDBETWEEN formula in excel to get the regression output in a meaningful manner. By analyzing the p value of each variable; it can be seen that the p valueof age, income and tenure is 0.00,which is lower than the significance value of 0.05, thus providing the strong statistical evidence of rejecting the null hypothesis which states that there is not any significant relationship between the profitability of the bank and age, income and tenure. In contradiction to this, the p value of the district is 0.45, which is greater than the significance level of 0.05, thus providing strong statistical evidence of rejecting the alternate hypothesis which states that there is a significant relationship between the profitability of the bank and the district.

### Data analysis with and without missing values

In the wake of the missing values in the data; it is found that there are 8289 missing values in the variable age,with an addition of 8262 missing values in the variable income. The difference in the data with missing values is compared with the data without the missing values,using the two sample t-test. Each of these two variables’ data has evaluated the difference in the data with missing values and without missing values.

### Age

The hypothesis of evaluating the difference in the data of age with missing values and without missing values,are generated below:

H0 = There is not any significant difference in the data of age with and without the missing values

H1 = There is a significant difference in the data of age with missing values and without the missing values…………………………

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