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Unformatted text preview: ACC649:CAISPRING 2011 DR. Samir El-Gazzar Review of basic statistical concepts Professor Kam C. Chan This is intended to be a review rather than a comprehensive discussion of basic statistical concepts. However, you must study the review materials in detail since they are related to an assignment and many assigned readings. 1. Test of sample mean 1.1 Research hypothesis I want to examine, in general, if my ACC 649 students performed significantly different in the final exam relative to the mid-term exam. Change in exam performance is defined as: (final exam grade mid-term exam grade) Change in grade = ---------------------------------------------------- (1) mid-term exam grade My research objective is stated as follows: H : average change in grade = 0 H 1 : average change in grade 0 H is called the null hypothesis. H 1 is called the alternative hypothesis. They always go together in a pair. Null hypothesis is the default position that there is no effect, change, or relationship in whatever someone wants to examine. In my case, the null hypothesis suggests that there is no significant average change in grades among my students. The alternative hypothesis is the effect that I want to prove. In my example, I want to examine if there is a significant average change in grades. Since the average change can be positive (final exam grade is higher than mid-term grade) or negative (final exam grade is lower than mid-term exam grade), the alternative hypothesis is stated as different from zero. There are two possible outcomes from my analysis. First, I can provide evidence that H 1 is most likely true and I can reject H . Second, I cannot provide sufficient evidence that H 1 is true and I cannot reject H . 1.2 Sample To examine my alternative hypothesis, I collected the grades for a sample of 20 students from my previous ACC 649 classes. A sample is a part of the population. In this example, I dont have the grade information for all of my previous ACC 649 students. I only randomly selected 20 of my former students in the sample. The main idea in statistical analysis is to use the data from a sample to infer the characteristics of the overall population. A sample is used since it is too costly or impossible to collect data for 1 the whole population. The population in this example is all of my ACC 649 students in the past 13 years at Pace. 1.3 Mean and standard deviation The following table shows the data. They are not real student grades. I just made up the data for illustration purposes. Student ID Mid-term Final Change in grade Change in grade - Mean (Change in grade - Mean) 2 1 80 82 0.02500000 0.01239955 0.00015375 2 65 80 0.23076923 0.21816878 0.04759762 3 84 80-0.04761905-0.06021950 0.00362639 4 53 57 0.07547170 0.06287125 0.00395279 5 90 88-0.02222222-0.03482268 0.00121262 6 88 91 0.03409091 0.02149046 0.00046184 7 54 52-0.03703704-0.04963749 0.00246388 8 78 66-0.15384615-0.16644661 0.02770447 9 74 79 0.06756757 0.05496711 0.00302138 10...
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- Spring '12