| Date | May 2015 | Marks available | 2 | Reference code | 15M.1.sl.TZ2.7 |
| Level | SL only | Paper | 1 | Time zone | TZ2 |
| Command term | Decide | Question number | 7 | Adapted from | N/A |
Question
The producer of a TV dancing show asked a group of 150 viewers their age and the type of Latin dance they preferred. The types of Latin dances in the show were Argentine tango, Samba, Rumba and Cha-cha-cha. The data obtained were organized in the following table.
A \({\chi ^2}\) test was carried out, at the 5% significance level.
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.
Markscheme
\({{\text{H}}_0}\) 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.
