Question

A Physics teacher takes a random sample of size 5 from his students. Their marks in a written test (x)

and a practical test (y) are given in the following table.

Student	A	B	C	D	E
X	11	14	16	12	15
Y	9	12	14	13	15

(i) Find the product moment correlation coefficient. [3]

(ii) Test, at the 5% significance level, whether there is evidence of positive correlation. [4]

The teacher takes a second random sample, this time of size 7, and the marks for this sample are summarised as follows.

Σx=96 Σx2 =1366 Σy=86 Σy2 =1096 Σxy=1220
(iii) Use the combined sample of size 12 to find the equation of the regression line of y on x, giving

your answer in the form y = px + q, where p and q are constants. [4]

One particular student scored 13 in the written test, but was absent for the practical test.

(iv) Estimate this student’s mark in the practical test and comment on the reliability of your estimate.

Answer 1