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

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 %

Explanation:

ΣX = 815

ΣY = 425

ΣX x Y = 34565

Σ = 67925

Σ
`$Y^2$` = 18699

So, correlation coefficient, b

`$b= (n \Sigma XY- \Sigma X \Sigma Y)/(√(n \Sigma X^2-( \Sigma X)^2) * √((n \Sigma Y^2 -(\Sigma Y)^2))$`

`$b = ((10 * 34565)-(815 * 425))/(√((10 * 67925)-(815)^2) * √((10 * 10699)-(425)^2))$`

`$b= -(725)/(9779 * 2702)$`

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.