# Pilgrim Bank Case Study

**Topics:**Statistical hypothesis testing, Normal distribution, Statistics

**Pages:**7 (600 words)

**Published:**May 25, 2015

September 26, 2013

How much do profits vary across customers? Provide statistical support for your answer. Out of a sample of 31,634 Pilgrim Bank customers, from a population of 5 million total, and zero missing values, profits vary widely. The average customer profitability is $111.50. The minimum value of this data set is -$221 and the maximum is $2071. This describes that there is a very wide range. The median customer profitability is $9 and the standard deviation is $272.84. See exhibit one.

How does Pilgrim Bank make money from its customers and how can this explain the variation in customer profitability? Pilgrim Bank makes its profit from customers with components including the balance in deposit accounts, the net interest spread, the fees collected by serving customers, and the interest from loans distributed. This can explain the variation in customer profitability because customer accounts generate different types of revenue for Pilgrim Bank. Each customer generates investment income by keeping a deposit balance. Fees are assessed for checking accounts, late payments and overdrafts. This is an important revenue source Pilgrim Bank. Since each customer varies in how many fees they rack up, each customer accounts for a different amount of the profitability from this source. Depending on the customer, a loan will be handled and the rate will be decided upon. Each customer would create revenue for the bank this way but not all would create the same amount.

Are online customers more profitable than offline customers? Provide statistical support for your answer. The null hypothesis is that online and offline customers are no different and the alternative hypothesis is that there is a difference between online and offline customers. According to the data, online and offline customers are no different. We accept the null hypothesis and the differences are not meaningful. Of the 31,634 customers in the sample, 3854 are online customers and the remaining are offline customers. The ranges of these two types of customers overlap. The customer profitability minimum for offline and online customers is -$221 and the maximum is approximately $2000 for both as well. The average profitability is approximately $113 and standard deviation is approximately 275 for both types. The median for offline customers is nine and for online customers in twelve. In a 95% confidence interval a two-sample t-test revealed that the p-value is 0.210. Since this p-value is greater than the significance level alpha of .05 we cannot reject the null hypothesis. See exhibit two through five.

What is the role of customer demographics in comparing online and offline profitability? Provide statistical support for your answer. No demographic plays a role in online and offline profitability. The R², or predictability factor, is 0.057. This is a weak correlation because it is nowhere near +/- one. Only age, income and tenure have a positive relationship with profit. See exhibit six and seven.

What is your recommendation to the senior management team in terms of Pilgrim Bank’s online channel pricing strategy? Should the bank charge fees, offer rebates or do nothing in regards to pricing for online channel use? My recommendation is for Pilgrim Bank to conduct more exploration and research into what makes a more profitable customer. Since we do not have an insight because no relationship exists between online use and profitability, we cannot leverage it using fees or rebates. Until Pilgrim Bank finds a relationship between a profitable customer and another factor, there should be no decision made by the group.

Exhibit 1:

Exhibit 2:

Exhibit 3:

Exhibit 4:

Exhibit 5:

Exhibit 6:

Exhibit 7:

Exhibit 8:

Please join StudyMode to read the full document