One Sample Hypothesis Testing Paper

Introduction

The data set of Century National Bank shows account balance in dollars, number of ATM transactions in the month, number of other bank services used, customers who use a debit card and those who do not, the accounts which receives interest, and city of origin. Century National Bank has a vast amount of account information to maintain. This one-sample hypothesis paper will formulate both a numerical and verbal hypothesis and show the five step hypothesis of the data that is acquired.

The experiment will also describe the results and findings of the hypothesis testing to answer the question above. This paper will analyze raw data tables and the results of the Z-test using both graphical and tabular methods.

Numerical and Verbal Hypothesis

According to Caroline Fouts (2008), "Debit cards have become a very popular way to pay for everything from fast food to rental cars." The Federal Reserve reports that debit card transactions have been growing more than 20% annually and have surpassed credit card transactions" (4).

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The appeal is understandable as debit cards are quick and convenient to use (Fouts, 2008). The Century National Bank Data Set will help us determine if the average balance of account holders is directly related to ownership of a debit card. The bank data will either allow us to accept or reject our hypothesis that the average balance of account holders with debit cards is lower than those without. The research for the hypothesis will be completed by calculating that average balances of customers with and comparing the average balances of those without debit cards.

The null hypothesis for the bank data set would be : the average balance of account holders with debit cards if higher than those without. If the data set does not prove the alternate, then we will have failed to reject the null hypothesis, however, if the team is able to prove the alternate we will reject the null, which stated accounts holders who use debit card carry higher balances to those who do not.

Five-Step Hypothesis Test

Testing a hypothesis requires one to follow five steps. These steps include: stating the null hypothesis; selecting a level of significance; identifying the test statistic; stating the decision rule; and taking a sample and arriving at a decision. One must properly identify the appropriate data and levels of measure for each test in order to reach an accurate conclusion of whether or not to reject or accept the null hypothesis. In this instance the null hypothesis ( ), concludes that the average balance in accounts with debit cards are higher than those without debit cards. The alternative hypothesis ( ), states that the average balance of accounts without debit cards is higher than those with debit cards.

The chosen level of significance for this test is 0.01, or 1%. This level of significance is known as , or alpha, stating that Learning Team A believes that we are 99% sure of our test results (Doan & Seward, 2007). The level of significance leaves a one percent probability of being incorrect in our findings thus making it more difficult to reject the null hypothesis. By making is harder to reject the null hypothesis, Learning Team A is attempting to reduce the possibility of manipulating the decision (Doan & Seward, 2007).

In this case, Learning Team A expects a 99 % chance that the null hypothesis will be accepted within this specific data sample of the Century National Bank customer population. The decision to reject or accept the null hypothesis may be different if an alternative sampling of the bank's population were provided as this sample may not be a true representation of the entire customer portfolio. For this experiment only 60 customers were sampled and our results are based on such sampling.

The third step of the hypothesis testing is identifying the test statistic. For this experiment, the Z statistic will be used because we can assume normality with the sample size. The specific value is calculated as , or 2.576, for 99% confidence in our testing (Doan & Seward, 2007). In this situation, Learning Team A would reject if . This figure represents step four in the hypothesis testing process: state the decision rule. Three types of decision rules exist: right-tailed, left-tailed, and two-tailed (Doan & Seward, 2007). The rule that fits our test demands that a right-tailed test is to be used because our critical value is a positive calculation.

The final step in testing a hypothesis is to select a sample and arrive at a decision. For this test, we will take the population with and without debit cards and compare the mean balances to uncover whether to reject the null hypothesis in favor of the alternate. Out of 60 customers 34 do not use a debit card. The mean account balance for those without debit cards (MegaStat) is $1,435.82. 26 out of 60 customers have a debit card. The mean account balance for those with debit cards is $1,583.62.

Test ResultsHypothesis: The average balance of account holders with debit cards is lower than those without.

Our research question, or alternate hypothesis, is that the average balance of customers with debits cards is lower than that of customer who does not have debit cards. In our research we found the opposite, i.e., the null hypothesis, to be accepted. Out of the 60 customers evaluated in this study, it was found that the 26 that do have debit cards have a higher balance than the 34 customers who do not. The account balance for customers with debit cards was over $100 more than those without.

We will use this information to show that our research question was disproved. Since some of our teammates are or were in the banking profession, and the fact that all have used or are currently using banking services, it is automatically assumed that because people have debit cards they are more likely to use the funds faster than those who do not, and therefore, have less money. But just the opposite proved to be true. Learning Team A will need to re-evaluate our hypothesis to look into how is it that people who have debit cards, and therefore, have faster access to their money, have more money available to them than those who don't.

References

Doan, D. & Seward, L. (2007). Applied Statistics in Business and Economics. Burr Ridge, IL:McGraw-Hill. Retrieved August 2, 2008, from https://mycampus.phoenix.eduFouts, C. (2008). Why should you never own a debit card. Retrieved on August 3, 2008,from http://www.creditsecretsbible.org