State suitable hypotheses.

The marks obtained by the 12 students who sat both papers are given in the following table. 

(i)     Determine the product moment correlation coefficient for these data and state its p-value.

(ii)     Interpret your p-value in the context of the problem.

George obtained a mark of 63 on Paper 1 but was unable to sit Paper 2 because of illness. Predict the mark that he would have obtained on Paper 2.

Another class of 16 students sat examinations in Physics and Chemistry and the product moment correlation coefficient between the marks in these two subjects was calculated to be 0.524. Using a 1 % significance level, determine whether or not this value suggests a positive association between marks in Physics and marks in Chemistry.

\({{\text{H}}_0}:\rho  = 0;{\text{ }}{{\text{H}}_1}:\rho  > 0\)     A1

[1 mark]

(i)     correlation coefficient = 0.905     A2

p-value \( = 2.61 \times {10^{ - 5}}\)     A2

(ii)     very strong evidence to indicate a positive association between marks in Mechanics and marks in Statistics     R1 

[5 marks]

the regression line of y on x is \(y = 8.71 + 0.789x\)     (M1)A1

George’s estimated mark on Paper 2 \( = 8.71 + 0.789 \times 63\)     (M1)

= 58     A1

[4 marks]

\(t = r\sqrt {\frac{{n - 2}}{{1 - {r^2}}}}  = 2.3019 \ldots \)     M1A1

degrees of freedom = 14     (A1)

p-value \( = 0.0186 \ldots \)     A1

at the 1 % significance level, this does not indicate a positive association between the marks in Physics and Chemistry     R1

[5 marks]