Can a pretest on mathematics skills predict success in a statistics course? the 55 students in an introductory statistics class took a pretest at the beginning of the semester. the least-squares regression line for predicting the score y on the final exam from the pretest score x was y = 10.5 + 0.82x . the product of 0.82 times x (the pre-test score) + 10.5 predicts the score on the final exam, y. the standard error of b was 0.38. test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative.

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3