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. 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.
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