Question

A teacher records the amount of time it took a random sample of students to finish a test and their scores on that test. Let x be the score and y be the amount of time. Conduct a hypothesis test of the claim that there is a linear correlation between the variables, using a 0.10 level of significance. Find the PERCENTAGE OF THE VARIANCE IN THE Y-VALUES THAT CAN BE EXPLAINED BY THEIR LINEAR RELATIONSHIP WITH THE X-VALUES.

Answer 1

Answer:

The question is incomplete. The complete table is:      

Score in percent (X): 80, 75, 70, 90, 95, 100, 75, 60, 75, 95

Time in minute (Y) : 45, 48, 40, 50, 40, 30, 30, 39, 38, 55

The answer is 0.55 %

Step-by-step explanation:

ΣX = 815

ΣY = 425

ΣX x Y = 34565

Σ = 67925

Σ$Y^2$ = 18699          

So, correlation coefficient, b

$b= \frac{n \Sigma XY- \Sigma X \Sigma Y}{\sqrt{n \Sigma X^2-( \Sigma X)^2} \times \sqrt{(n \Sigma Y^2 -(\Sigma Y)^2}}$

$b = \frac{(10 \times 34565)-(815 \times 425)}{\sqrt{(10 \times 67925)-(815)^2} \times \sqrt{(10 \times 10699)-(425)^2}}$

$b= -\frac{725}{9779 \times 2702}$

b = -0.0741

Correlation Determination:

$B^2 = (-0.0741)^2$

    = = 0.0055 = 0.55%

Therefore,  0.55 percentage of the variation in y can be explained by x variable.