A Physics teacher takes a random sample of size 5 from hisstudents. 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 isevidence 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 ofthe 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 wasabsent for the practical test.
(iv) Estimate this student’s mark in the practical test andcomment on the reliability of your estimate.
