(i)     Calculate the correlation coefficient for this sample.

(ii)     Calculate the $p$-value of your result and interpret it at the $1\%$ level of significance.

(i)     Calculate the equation of the least squares regression line of $w$ on $h$ .

(ii)     The height of a randomly selected boy of this age of $90$ cm. Estimate his weight.

(i)     $r = \frac{{34150 - 340 \times \frac{{2002}}{{20}}}}{{\sqrt {\left( {5830 - \frac{{{{340}^2}}}{{20}}} \right)} \left( {201124 - \frac{{{{2002}^2}}}{{20}}} \right)}}$     (M1)(A1)

Note: Accept equivalent formula.

$= 0.610$     A1

(ii)     ($T = R \times \sqrt {\frac{{n - 2}}{{1 - {R^2}}}}$ has the t-distribution with $n - 2$ degrees of freedom)

$t = 0.6097666 \ldots \sqrt {\frac{{18}}{{1 - 0.6097666{ \ldots ^2}}}}$     M1

$= 3.2640 \ldots$     A1

${\rm{DF}} = 18$     A1

$p{\rm{ - value}} = 0.00215 \ldots$     A1

this is less than $0.01$, so we conclude that there is a positive association between heights and weights of boys of this age     R1

[8 marks]

(i)     the equation of the regression line of $w$ on $h$ is

$w - \frac{{340}}{{20}} = \left( {\frac{{20 \times 34150 - 340 \times 2002}}{{20 \times 201124 - {{2002}^2}}}} \right)\left( {h - \frac{{2002}}{{20}}} \right)$     M1

$w = 0.160h + 0.957$     A1

(ii) putting $h = 90$ , $w = 15.4$ (kg)     A1

Note: Award M0A0A0 for calculation of $h$ on $w$.

[3 marks]