Write down the null hypothesis for this test.

Write down the observed number of viewers who preferred Rumba and were older than 20 years old.

Use your graphic display calculator to find the $p$-value for this test.

The producer claims that the type of Latin dance a viewer preferred is independent of their age.

Decide whether this claim is justified. Give a reason for your decision.

${{\text{H}}_0}$ the type of Latin dance the viewer prefers is independent of their age     (A1)     (C1)

Notes: Accept “not dependent” or “not associated”. Do not accept “not correlated” or “not related” or “not connected”.

$18$     (A1)     (C1)

$p = 0.0876\;\;\;(0.0875813 \ldots )$     (A2)     (C2)

Notes: Award (A2) for $0.088$.

Award (A1)(A0) for an answer of $0.0875$.

$0.05 <$ their $p$-value     (R1)

the producer’s claim is justified     (A1)(ft)     (C2)

Notes: Do not award (R0)(A1)(ft). Follow through from their answer to (c). If there is no answer in part (c), award (R1)(A0) for stating the relationship between the independence and the $p$-value compared to $0.05$.

If (R1) is awarded, award (A1)(ft) for the answer ‘yes’ or the answer ‘no’ if it is consistent with their reasoning.

Similarly, allow ‘accept ${{\text{H}}_0}$’ or ‘reject ${{\text{H}}_0}$’ if consistent with their reasoning.

Award (R0) for comparing $p$ with the critical value.