State suitable hypotheses for this investigation.

State, in context, what conclusion should be drawn from this $p$-value.

The teacher then asks Anne for the values of the $t$-statistic and the product moment correlation coefficient $r$ produced by the calculator but she has deleted these. Starting with the $p$-value, calculate these values of $t$ and $r$.

${H_0}:\rho  = 0;{\text{ }}{H_1}:\rho  > 0$     A1

Note:     Do not accept $r$ in place of $\rho$.

[1 mark]

insufficient evidence to conclude that there is a (positive) association between marks in these two subjects (or equivalent statement in context)     A1

[1 mark]

degrees of freedom $= 10$     (A1)

required value of $t = {\text{inverse }}t(0.823)$     (M1)

$= 0.972$     A1

attempt to solve $t = r\sqrt {\frac{{n - 2}}{{1 - {r^2}}}}$     (M1)

$r = 0.294$     A1

Note:     Accept any $r$ value that rounds to 0.29.

Note:     Follow through their $t$ value to determine $r$.

[5 marks]