Is there a relationship between GRE total scores and GPAs in the master’s programs in electrical engineering?

Question asked: A researcher asks the question “Is there a relationship between GRE total scores and GPAs in the master’s programs in electrical engineering?” The researcher’s null hypothesis states, “There is no correlation between GRE total score and GPA from an electrical engineering master’s program.” The researcher’s alternative hypothesis states, “There is a positive correlation between GRE total scores and GPA from an electrical engineering master’s program.” Are these valid hypotheses for the research question? Why or why not? What other observations can you make regarding the hypotheses and research question?

My response: The research question is “Is there a relationship between GRE total scores and GPAs in the master’s programs in electrical engineering?” The question is not asking as to positive or negative relationship but any relationship (positive or negative). Thus the research question will be answered in the affirmative, that is, if one can establish that there is either a positive or a negative correlation between GRE total scores and GPAs in the master’s programs in electrical engineering. This is therefore, a two tailed test:

Null Hypothesis: There is no correlation between GRE total score and GPA from an electrical engineering master’s program.

Alternative Hypothesis: There is a correlation between GRE total score and GPA from an electrical engineering master’s program.

Null Hypothesis: Correlation = 0

Alternative Hypothesis: Correlation ≠ 0

In a hypothesis test, two opposing hypotheses are examined: the Null Hypothesis and the Alternative Hypothesis (Johnson, et. al., 2001).
The Null Hypothesis is the statement that is tested. It is the opposite of what the researcher sets out to conclude. Here the research question is whether there is a relationship between GRE scores and GPA- is there a correlation between them? The opposite of this is that there is no correlation. This is the Null Hypothesis. Correlation = 0.

The alternative hypothesis is the one that the researcher would want to be able to conclude as true (Gravetter & Wallnau, 2010). In this case the researcher would want to establish that there is a correlation between GRE scores and GPA. Correlation ≠ 0. The hypothesis are valid because a hypothesis is just an assumption that is yet to be proved, with the null hypothesis being a negative statement while the alternative one being a positive statement. The mentioned hypothesis seems to be a valid hypothesis according to this research question. As the GRE total increases, the GPA’s is also expected to increase.

Question professor asked that I request an answer to: Very good analysis and recommendations, Janet! Good assessment on the proposed hypotheses and how these should be handled. You are correct that in this particular case we either have directional hypotheses or non-directional ones but not a combination of the two which is what the question poses. In this case, the hypotheses are not valid but these can be easily corrected by the proposal you make. Based on your understanding of the topic, would you say that the study is better executed if a non-direction set of hypotheses is used? Why or why not?

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