Hypothesis Testing Essay

Hypothesis Testing Essay.

Hypothesis Testing Essay. The purpose of hypothesis testing is to allow an individual to choose between two different hypotheses pertaining to the value of a population parameter. Learning team C has conducted a hypothesis test surrounding the amount of time spent on homework by males and females, and will address if there is a correlation between the variables. Additionally, learning team C will determine if there is a positive or negative correlation, and how strong that correlation is between both variables. Overall, statistics can be very challenging and we will share some of the most puzzling concepts experienced in Quantitative Analysis for Business thus far.

Hypothesis Testing Essay

When conducting a hypothesis test, it is imperative that a null hypothesis is identified. The null hypothesis is the hypothesis that is assumed to be true unless there is sufficient enough evidence to prove that it is false (McClave, 2011). The null hypothesis for this experiment: Is the mean amount of time spent on homework by females equal to the amount of time spent on homework by males? The observed significance level is .

05, which means that there is a five percent chance that we will reject the null hypothesis, even when it is true. The activity data set provided were eight data points for women and six data points for men.

Because of the small sample size, we have conducted a t-test for this experiment. The degrees of freedom equal twelve, which we assign a critical value of 2.179 from a t-table. If the test statistic (t-statistic) is less than -2.179, or greater than 2.179 we will reject the null hypothesis in favor of the alternative. The t-statistic for the time spent on homework by men and women is -.4899. This figure does not fall into the rejection region, so we fail to reject the null hypothesis. In other words, the mean amount of time spent on homework by men and women are equal with a ninety-five percent confidence level. We have also determined the correlation coefficient. The correlation coefficient (denoted by the letter r) is the measure of the degree of linear relationship between two variables (Webster.edu, n.d.). The correlation coefficient can be any value between negative one and one. If the correlation coefficient sign is negative, it means that as one variable decreases the other variable increases. The opposite is true for a positive correlation coefficient, if the value of one variable increases the other variable decreases. It is important to note that correlation does not necessarily mean causation; we cannot assume a correct conclusion based on correlation alone.

For this experiment, the correlation between men and women was 0.346102651. When data with values of r are close to zero, they show little to no straight-line relationship (Taylor, 2015). Even though the correlation for this experiment was positive, it is not a strong correlation. The closer the value of r to zero means that there is a greater variation around the line of best fit (Laerd Statistics, 2015). Statistics can be a very daunting subject, and there have been some concepts that have proven to be difficult for each member of learning team C. Many team members struggle with the proper selection of formulas in Microsoft Excel, while others struggle to substitute values into the many equations involved in statistics. There are also numerous symbols to remember, and properly identify when computing an equation.

From a conceptual standpoint, probability is tough topic to grasp. The concept itself seems unintuitive, and is difficult to understand an intangible concept that is based on guessing and the best chance that an individual has to experience one event or another is random (probability). When you take that concept and try to make it tangible by putting it into an equation, things get quite confusing. Hypothesis testing can be beneficial when an individual is trying decide on what hypothesis to choose pertaining to the value of a population parameter. When deciding to conduct hypothesis testing it is important to go through the five steps of the hypothesis testing procedure that include: making assumptions, stating the null and alternate hypothesis, determining the correct test statistic and sampling distribution, computing the test results, and interpreting the decision (Boston University, n.d.).

Interpreting the decision can include comparing the means for each of the groups can give a better understanding of where each group falls as an average. Interpreting the decision also includes determining whether there is a correlation between the two variables and determining whether the correlation is positive or negative. For this experiment, the goal was to determine if there was a significant difference for time spent doing homework by males and females. Hypothesis testing is used to determine if there is enough statistical evidence to support a certain belief about a parameter.

References
Boston University. (n.d.). The 5 steps in hypothesis testing. Retrieved from Boston University, website. Laerd Statistics. (2015). Pearson-product moment correlation. Retrieved from https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php McClave, J. T. (2011). Statistics for business and economics (11th ed.). Boston, MA: Pearson Education. Taylor, C. (2015). How to calculate the correlation coefficient. Retrieved from http://statistics.about.com/od/Descriptive-Statistics/a/How-To-Calculate-The-Correlation-Coefficient.htm Webster.edu. (n.d.). Correlation. Retrieved from http://www2.webster.edu/~woolflm/correlation/correlation.html

Hypothesis Testing Essay

One Sample Hypothesis Testing Paper Essay

One Sample Hypothesis Testing Paper Essay.

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).

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

You may also be interested in the following: sample reaction paper, sample of reaction paper, reaction paper sample, sample reaction paper, sample of reaction paper, reaction paper sample

One Sample Hypothesis Testing Paper Essay