(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student.
\[\begin{array} { l l l l l }
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
2 . & \text { Stanford } & 665 & 10.2 & 60,000 \
3 . & \text { Penn } & 644 & 19.4 & 55,000 \
4 . & \text { Northwestern } & 640 & 22.6 & 54,000 \
5 . & \text { MIT } & 650 & 21.3 & 57,000 \
6 . & \text { Chicago } & 632 & 30.0 & 55,269 \
7 . & \text { Duke } & 630 & 18.2 & 53,300 \
8 . & \text { Dartmouth } & 649 & 13.4 & 52,000 \
9 . & \text { Virginia } & 630 & 23.0 & 55,269 \
10 . & \text { Michigan } & 620 & 32.4 & 53.300 \
11 . & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
14 . & \text { UNC } & 625 & 15.4 & 50,800 \
15 . & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
16 . & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
21 . & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
23 . & \text { Georgetown } & 617 & 31.7 & 45,156 \
24 . & \text { Maryland } & 593 & 28.1 & 42,925 \
25 . & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\]
The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using the 25 data points in the table are shown below.
$$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of $t = 6.67$.
A) There is evidence (at $\alpha = .05$ ) of at least a positive linear relationship between SALARY and GMAT.
B) We estimate SALARY to increase $\$ 6.67$ for every 1-point increase in GMAT.
C) There is evidence (at $\alpha = .05$ ) to indicate that $\beta _ { 1 } = 0$.
D) Only $6.67 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight-line model.

Question

(Situation P) Below are the results of a survey of America's best graduate and professional schools. The top 25 business schools, as determined by reputation, student selectivity, placement success, and graduation rate, are listed in the table.
For each school, three variables were measured: (1) GMAT score for the typical incoming student; (2) student acceptance rate (percentage accepted of all students who applied); and (3) starting salary of the typical graduating student. 
\[\begin{array} { l l l l l } 
& \text { School } & \text { GMAT } & \text { Acc. Rate } & \text { Salary } \
\hline\text { 1. } & \text { Harvard } & 644 & 15.0 \% & \$ 63,000 \
2 . & \text { Stanford } & 665 & 10.2 & 60,000 \
3 . & \text { Penn } & 644 & 19.4 & 55,000 \
4 . & \text { Northwestern } & 640 & 22.6 & 54,000 \
5 . & \text { MIT } & 650 & 21.3 & 57,000 \
6 . & \text { Chicago } & 632 & 30.0 & 55,269 \
7 . & \text { Duke } & 630 & 18.2 & 53,300 \
8 . & \text { Dartmouth } & 649 & 13.4 & 52,000 \
9 . & \text { Virginia } & 630 & 23.0 & 55,269 \
10 . & \text { Michigan } & 620 & 32.4 & 53.300 \
11 . & \text { Columbia } & 635 & 37.1 & 52,000 \
\text { 12. } & \text { Cornell } & 648 & 14.9 & 50,700 \
\text { 13. } & \text { CMU } & 630 & 31.2 & 52,050 \
14 . & \text { UNC } & 625 & 15.4 & 50,800 \
15 . & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \
16 . & \text { UCLA } & 640 & 20.7 & 51,494 \
\text { 17. } & \text { Texas } & 612 & 28.1 & 43,985 \
\text { 18. } & \text { Indiana } & 600 & 29.0 & 44,119 \
\text { 19. } & \text { NYU } & 610 & 35.0 & 53,161 \
\text { 20. } & \text { Purdue } & 595 & 26.8 & 43,500 \
21 . & \text { USC } & 610 & 31.9 & 49,080 \
\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \
23 . & \text { Georgetown } & 617 & 31.7 & 45,156 \
24 . & \text { Maryland } & 593 & 28.1 & 42,925 \
25 . & \text { Rochester } & 605 & 35.9 & 44,499
\end{array}\] 
The academic advisor wants to predict the typical starting salary of a graduate at a top business school using GMAT score of the school as a predictor variable. A simple linear regression of SALARY versus GMAT using the 25 data points in the table are shown below. 
$$\beta _ { 0 } = - 92040 \quad \hat { \beta } _ { 1 } = 228 \quad s = 3213 \quad r ^ { 2 } = .66 \quad r = .81 \quad \mathrm { df } = 23 \quad t = 6.67$$
-For the situation above, give a practical interpretation of $t = 6.67$.
A) There is evidence (at $\alpha = .05$ ) of at least a positive linear relationship between SALARY and GMAT.
B) We estimate SALARY to increase $\$ 6.67$ for every 1-point increase in GMAT.
C) There is evidence (at $\alpha = .05$ ) to indicate that $\beta _ { 1 } = 0$.
D) Only $6.67 \%$ of the sample variation in SALARY can be explained by using GMAT in a straight-line model.

Quizplus · Accepted Answer

There is evidence (at $\alpha = .05$ ) of at least a positive linear relationship between SALARY and GMAT.

(Situation P) Below Are the Results of a Survey of America's