This was the question: Assume that you are interested in the relationship between Graduate Record Examinations (GRE) scores (the total of all subtests) and graduate school grade point averages (GPAs) at the end of their graduate programs. Conveniently, you have access to the GRE scores and GPAs of a large number of graduate students who have graduated from the electrical engineering master’s program in an Ivy League university between 2000 and 2013. The Pearson correlation coefficient did not reach significance. What can you conclude from the data analysis? Can the result be generalized to all graduate students in electrical engineering master’s programs across the United States? Why or why not?My response: Assuming the following hypothesesH0: p=0 (GRE and GPA scores are not linearly uncorrelated)H1:p=/=0 (GRE and GPA scores are linearly correlated)It is stated that Pearson correlation coefficient test is not significant (p value not less than significance level), and therefore, H0 cannot be rejected (Cowan, 1998). Thus, there is insufficient sample evidence to conclude that GRE and GPA scores are linearly correlated. The result cannot be generalized because the sample consists of students of electrical engineering master program and that too of a particular university, and thus, the sample is not representative of the population. From the given the information by the Pearson correlation coefficient that there is not a significant relationship between GRE scores and GPAs as seen in the Ivy League university in the stated years cannot be used to generalize the results of all the students in the electrical engineering graduates. This is mainly because of possibilities of the existence of some non-linear relationship between the two variables since the Pearson Correlation coefficient is involved mainly in the measuring of the linear relation (Gravetter & Wallnau, 2010). Hence, the non-linear relations existing between the two variables cannot make sense using the Pearson correlations.Professor asked this question and this is the question I need an answer to: Thank you Janet for your feedback and recommendations. In your analysis you point to ‘linear correlation’ or ‘not linear correlation’ but why do you believe the relationship has to be linear? Couldn’t we have a relationship versus no relationship? In this case we confirm that the relationship is not statistically significant which leads to ‘chance’ but there is not enough information that points to having a linear versus a non-linear relationship. Thoughts?
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