Question

1. Imagine you work as an analyst for a local school district. The district administers a final examination to its high school students that is required before graduation. Because the exam is very important, students are given a practice test the year before. The school district is interested in how well the practice test serves as an indicator of final exam performance. You collect some data and conduct some analyses (below). Use that information to inform the school board what a student achieving a passing grade on the practice exam (score of 70) predicts about their performance on the final exam.

Practice Exam      Actual Exam

           80                            75    

           63                            81

           42                            51

           92                            86

           84                            47

           38                            30

Avg = 66.5                  Avg = 61.7

StDev= 20.7            StDev = 20.3

                     r = + .65

Answer 1

Avg for X = 66.5

StDev for X= 20.7                 

Avg for Y = 61.7

StDev for Y = 20.3

r = + .65

b= 0.65*20.3/20.7

b= 0.637

a=61.7-0.637*66.5

a=61.7-42.36

a= 19.34

y= a+bx

y= 19.34+0.637*x

For x= 70

y= 19.34+0.637*70

y(hat)= 63.93

y(hat)= 64.