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

question 22

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(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.  School  GMAT  Acc. Rate  Salary  1.  Harvard 64415.0%$63,0002. Stanford 66510.260,0003. Penn 64419.455,0004. Northwestern 64022.654,000 5.  MIT 65021.357,0006. Chicago 63230.055,2697. Duke 63018.253,300 8.  Dartmouth 64913.452,0009. Virginia 63023.055,269 10.  Michigan 62032.453.300 11.  Columbia 63537.152,000 12.  Cornell 64814.950,700 13.  CMU 63031.252,050 14.  UNC 62515.450,800 15.  Cal-Berkeley 63424.750,000 16.  UCLA 64020.751,494 17.  Texas 61228.143,985 18.  Indiana 60029.044,119 19.  NYU 61035.053,161 20.  Purdue 59526.843,500 21.  USC 61031.949,080 22.  Pittsburgh 60533.043,500 23.  Georgetown 61731.745,15624. Maryland 59328.142,92525. Rochester 60535.944,499\begin{array} { l l l l r } & \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 \\\text { 5. } & \text { MIT } & 650 & 21.3 & 57,000 \\6 . & \text { Chicago } & 632 & 30.0 & 55,269 \\7 . & \text { Duke } & 630 & 18.2 & 53,300 \\\text { 8. } & \text { Dartmouth } & 649 & 13.4 & 52,000 \\9 . & \text { Virginia } & 630 & 23.0 & 55,269 \\\text { 10. } & \text { Michigan } & 620 & 32.4 & 53.300 \\\text { 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 \\\text { 14. } & \text { UNC } & 625 & 15.4 & 50,800 \\\text { 15. } & \text { Cal-Berkeley } & 634 & 24.7 & 50,000 \\\text { 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 \\\text { 21. } & \text { USC } & 610 & 31.9 & 49,080 \\\text { 22. } & \text { Pittsburgh } & 605 & 33.0 & 43,500 \\\text { 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. β0=92040β^1=228s=3213r2=.66r=.81df=23t=6.67\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
-A 95% prediction interval for SALARY when GMAT = 600 is ($37,915, $51,948) . Interpret this interval for the situation above.

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Definitions:

Marginal Product

The increase in output that results from employing one more unit of a particular input, holding all other inputs constant.

Total Product

The total quantity of output produced by a firm from a given quantity of inputs during a certain period of time.

Workers

Individuals engaged in some form of employment or labor, contributing their skills or effort in exchange for compensation.

Marginal Product

The additional output that is produced by adding one more unit of a specific input, while keeping other inputs constant.

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