Statistics Assignment | Statistical Analysis Assignment
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Added on 2020-05-11
Statistics Assignment | Statistical Analysis Assignment
Added on 2020-05-11
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IntroductionXYZ University has send questionnaire to 100 graduates from four disciplines which pertainsto questions in relation to their employment status and salary level. However, only 648graduates have responded to the survey. Using the available sample data along with suitableinferential techniques (hypothesis testing), the objective of this report is to test the variousclaims that have been presented. The given report would be submitted to the Director of thecareer centre at the University and perhaps would help the University and the future studentsin order to make prudent career choices based on their underlying objective. Statistical AnalysisAs highlighted in the previous section, there are certain questions which need to be answeredbased on the given sample responses that have been collected from past students. It isapparent that the objective of the given statistical analysis is to opine on the population trendsand the same has to be based on the sample information made available. As a result, therelevant statistical techniques would be those that are fall under inferential statistics. The keytechnique that would be deployed here is the testing of hypothesis using suitable tests basedon the underlying situation and satisfaction of corresponding assumptions.Employment Status ComparisonIt needs to be answered whether the employment status across the four group of graduates isstatistically different or not. It is apparent that the employment status is essentially categoricaldata which is represented in the form of numerical values. The appropriate test deployed forthe same would be ANOVA single factor as the underlying means of the four graduatedisciplines need to be compared to determine if there is any significant difference betweenthese or not. An alternative in the form of T test cannot possibly be used here as the numberof variables whose average need to be compared are only four but a T test could only test thesame for two variables at a time. In total there are 648 samples which are distributed acrossthe four disciplines. Also, the samples in the various disciplines would be independentsamples as the underlying disciplines, interests and intellectual capabilities of the graduateswould not be dependent on each other.For the ANOVA test, the following assumptions ought to be satisfied.
The group sample needs to be drawn from a population that is normal.The underlying populations tend to have a common variance.The samples drawn are independent.With regards to the population being sample, it is apparent that the questionnaire was sent to1000 graduates but the method of selection of these graduates has not been outlined. It can beeither assumed that this constitutes the total graduates which passed in a particular year or thesample of these 1000 was randomly drawn. Thus, assuming the above, the population can beconsidered as normal. The samples drawn seem to be independent as 648 graduatesresponded to the survey and based on the given information, it can be assumed that neither ofthese was contacted by the university personally. Besides, in terms of population variance,the sample variances are different and if the F test is used to compare the variances of each ofthe two sample (according to discipline), the variance of the population would not come to besame. However, despite the above, the ANOVA test is being applied in the given case.Null Hypothesis (H0): μhealth= μCommerce= μLaw= μEngineering i.e. the employment status across thevarious graduate discipline does not alter in a statistical significant manner. Alternative Hypothesis (H1): Atleast one of the graduate disciplines would have anemployment status that is different from others in a statistical significant manner. From the excel, it is apparent that SST = 1.1985Also, from the excel SSE = 241.76It is known that MST=SSTDegreeofFreedomTreatment=1.19854−1=0.3995Also, it is known that MSE = SSEDegreeofFreedomError¿241.76648−4=0.3754Fstatistic=MSTMSE=(0.39950.3754)=1.064The above value needs to be compared with the critical value of F. Assuming a level of significance of 5% and df1= (4-1) = 3 and df2= (648-4) = 644, using theF table, the critical value comes out as 2.619
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