One Sample Hypothesis Testing Paper
Century National Bank
Yuri Sanchez, Ph.D
November 3, 2008
A learning team from the University of Phoenix researched a problem that was presented from Century National Bank. Century National Bank conducted a study in regards to the use of its automatic teller machines (ATMs). Of particular interest is whether accountholders with balances less $1000, those with balances between $1000 and $2000, and those with balances over $2000 are most likely to execute a bank transaction using the machines.
To investigate further, samples of customers in each of the categories were selected. The number of ATM transactions last month was determined for each of the selected categories, and the results are shown below. At the .05 significance level bank management has requested the team conclude which category of accountholders is more likely to execute a bank transaction using the ATMs most.
When looking at the data presented the first hypothesis would lead most to believe that the accountholders with balances between 1000 and 2000 execute the most transactions using ATMs. In order to draw the strongest possible inferences to that hypothesis, it is imperative that the team utilizes the “Five-Step Process for Hypothesis Testing”, and narrow down the hypothesis to fit the standards for one-sample hypothesis testing.
Numerical & Verbal Hypothesis Statement
Based upon the data provided and the request from Century National Bank’s management the team has developed the following research question:
Are Century National Bank account holders with balances less than or equal to $2000 more likely to execute a bank transaction using ATMs then those with more than $2000?
When doing research the Team developed the following hypothesis.
• Null Hypothesis: Account holders that have 2000 dollars are more likely to use the ATM during the Month
Our numerical statement would be stated as follows:
• Ho: μ < 2000
• Ha: μ > 2000
The Five-Step Procedure for Hypothesis Testing
When developing a research project the hypothesis is the key element to defining and developing the project. Testing the hypothesis is the single most important step to developing the project. If the testing is not done correctly then the entire project can flow in the wrong direction and the project could be a failure. Researchers have developed a five step process to assure that process of testing the hypothesis is performed correctly and uniformly.
The first step in the testing procedure is to state the null hypothesis and the alternate hypothesis. The null hypothesis is always one of status quo or no difference. The null hypothesis is represented as H0 (H sub zero). It is the hypothesis that contains an equal sign. Researchers often anticipate that the null hypothesis will fail. (Lind, Marchal, & Wathen, 2005)
Using the data given from the Century National Bank Research Team B has conducted, the null hypothesis, or status quo, the team established was: Account holders that have 2000 dollars are more likely to use the ATM during the month or Ha: μ > 2000.
The second step in the testing procedure is to select a level of significance (ά or alpha) which will be used when finding critical value(s). The level of significance chosen indicates how confident the researcher is when making the decision. Common significance levels are .01, .05, and .10. It is important to always state the chosen level of significance
Team B chose to select a level of significance (ά or alpha) of .05. According to D.A. Lind, W.G. Marchal, & S.A. Wathen, Text book Statistical techniques in business and economics (2005) “A .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong.”
Step three of the hypothesis testing is to identify the test...
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