TO: Bank X
FROM: Scott Hebert
DATE: April 30, 2009
SUBJECT: Cash Back Options Analysis
After much deliberation, the executive team at Bank X has decided to utilize some form of cash back option for their new credit card offering. The choices have been narrowed down to offering cash back on either purchases made online or purchases made at clothing stores. Therefore, the research question that needs to be addressed is, do customers spend more money shopping online or at clothing stores? With that question in mind, we can begin the process of creating hypotheses and performing the necessary statistical analysis.
Bank X wants to know if the proportion of money spent online is greater than or less than the money spent at clothing stores. In order to test this hypothesis, a null hypothesis (H0) must be developed to test against. The null hypothesis always claims that some population parameter is equivalent to a specific value. It is important to note that the null hypothesis is always a specific value that can either be accepted or rejected. This ensures the statistical analysis is performed on a single distribution (Triola, 2008). In this case, we wants to prove that the proportion of online shopping to clothing store shopping is not equal to 0.5. Therefore, the null hypothesis can be stated as p = 0.5.
As you can see, the null hypothesis states that online spending and clothing store spending are equivalent. This is a value that can be statistically tested. Once the analysis is complete, we will either accept or reject the null hypothesis. If the null hypothesis is rejected, Bank X will know that they must then strive to discover which form of shopping is preferred. The goal of hypothesis testing is to apply our test to a hypothesis that we hope to reject. The rejection of that hypothesis naturally leads to the support of the hypothesis we were striving to prove all along.
Triola, M. F. (2008). Elementary statistics (10th ed.). Boston: Pearson.