| Date | May 2008 | Marks available | 1 | Reference code | 08M.1.sl.TZ1.5 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Write down | Question number | 5 | Adapted from | N/A |
Question
\(200\) people of different ages were asked to choose their favourite type of music from the choices Popular, Country and Western and Heavy Metal. The results are shown in the table below.
It was decided to perform a chi-squared test for independence at the \(5\% \) level on the data.
Write down the null hypothesis.
Write down the number of degrees of freedom.
Write down the chi-squared value.
State whether or not you will reject the null hypothesis, giving a clear reason for your answer.
Markscheme
Choice of music is independent of age. (A1) (C1)
[1 mark]
\((3 - 1)(3 - 1)\)
\( = 4\) (A1) (C1)
[1 mark]
\({\chi ^2} = 51.6\) (A2) (C2)
Note: \(52\) is an accuracy penalty (A1)(A0)(AP).
[2 marks]
\(p{\text{-value}} < 0.05\) for \(5\% \) level of significance (R1)(ft)
or \(51.6 > {\chi ^2}_{crit}\)
Reject the null hypothesis (do not accept the null hypothesis). (A1)(ft) (C2)
Note: Do not award (R0)(A1).
[2 marks]
Examiners report
Candidates either gained good marks for this question or almost no marks depending on their preparation. It was obvious that some schools had omitted this from their programme. Candidates generally gave a reason for their conclusion in part (d) though some compared the chi-squared value with the \(p\)-value, resulting in the loss of both marks.
Candidates either gained good marks for this question or almost no marks depending on their preparation. It was obvious that some schools had omitted this from their programme. Candidates generally gave a reason for their conclusion in part (d) though some compared the chi-squared value with the \(p\)-value, resulting in the loss of both marks.
Candidates either gained good marks for this question or almost no marks depending on their preparation. It was obvious that some schools had omitted this from their programme. Candidates generally gave a reason for their conclusion in part (d) though some compared the chi-squared value with the \(p\)-value, resulting in the loss of both marks.
Candidates either gained good marks for this question or almost no marks depending on their preparation. It was obvious that some schools had omitted this from their programme. Candidates generally gave a reason for their conclusion in part (d) though some compared the chi-squared value with the \(p\)-value, resulting in the loss of both marks.
