It is believed that GPA (grade point average, based on a four-point scale) shoul

Question

It is believed that GPA (grade point average, based on a four-point scale) should have a positive linear relationship with ACT scores. Given below is the Microsoft Excel output for predicting GPA using ACT scores based a data set of eight randomly chosen students from a Big Ten university. What are the decision and conclusion on testing whether there is any linear relationship at 1% level of significance between GPA and ACT scores? Do not reject the null hypothesis: hence there is insufficient evidence to show that ACT scores and GPA are linearly related. Reject the null hypothesis: hence there is sufficient evidence to show that ACT scores and GPA are linearly related. Do not reject the null hypothesis: hence there is sufficient evidence to show that ACT scores and GPA are linearly related. Reject the null hypothesis: hence there is insufficient evidence to show that ACT scores and GPA are linearly related.

Explanation / Answer

To test whether there is any linear relationship between GPA and ACT scores,

i.e to test H0 : no linear relationship between GPA and ACT scores

against H1 : there is linear relationship between GPA and ACT scores

Since p-value = 0.0286 > 0.01,

So at 1% level of significance, we fail to reject H0 and we can conclude that there is insufficient evidence to show that ACT and GPA are linearly related.

ans) 1st option

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