A dean of a business school has fit a regression model to predict college GPA ba

Question

A dean of a business school has fit a regression model to predict college GPA based on a student's SAT score (SAT_Score), the percentile at which the student graduated high school (HS_Percentile) (for instance, graduating 4th in a class of 500 implies that 496 other students are at or below that student, so the percentile is 496/500 times 100 = 99), and the total college hours the student has accumulated (Total_Hours). The regression results are shown below. For testing the hypothesis that Total Hours has a significant relationship with GPA (refer to an earlier problem), what would be the conclusion at the 0.05 level of significance, in the context of the problem? Read carefully. Fail to reject the null hypothesis and conclude that beta_3 = 0. Reject the alternative hypothesis and conclude that Total_Hours has a relationship with GPA, and is therefore potentially useful for predicting GPA. Reject the null hypothesis and conclude that Total_Hours has a relationship with GPA, and is therefore potentially useful for predicting GPA Fail to reject the null hypothesis and conclude that Total_Hours equals 0. Fail to reject the null hypothesis. We cannot conclude that Total_Hours has relationship with GPA, and therefore we cannot conclude that it is potentially useful for predicting GPA. Reject the null hypothesis and conclude that Total Hours does not have a relationship with GPA, and is therefore not potentially useful for predicting GPA.

Explanation / Answer

Since the p-value of Total_hours is less than 0.05, there is no evidence to accept the null hypothesis.

Answer:

c) Reject the null hypothesis and conclude that Total_hours has a relationship with GPA, and is therefore potentially useful for predicting GPA.

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