| Date | May 2017 | Marks available | 2 | Reference code | 17M.1.sl.TZ1.6 |
| Level | SL only | Paper | 1 | Time zone | TZ1 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
In a school, students in grades 9 to 12 were asked to select their preferred drink. The choices were milk, juice and water. The data obtained are organized in the following table.
A \({\chi ^2}\) test is carried out at the 5% significance level with hypotheses:
\[\begin{array}{*{20}{l}} {{{\text{H}}_{\text{0}}}{\text{: the preferred drink is independent of the grade}}} \\ {{{\text{H}}_{\text{1}}}{\text{: the preferred drink is not independent of the grade}}} \end{array}\]
The \({\chi ^2}\) critical value for this test is 12.6.
Write down the value of \(x\).
[1]
a.
Write down the number of degrees of freedom for this test.
[1]
b.
Use your graphic display calculator to find the \({\chi ^2}\) statistic for this test.
[2]
c.
State the conclusion for this test. Give a reason for your answer.
[2]
d.
Markscheme
30 (A1) (C1)
[1 mark]
a.
6 (A1) (C1)
[1 mark]
b.
\({\text{19.0 (18.9640)}} \ldots \) (A2)(ft) (C2)
Note: Follow through from part (a).
Award (A1) for truncation to 18.9.
[2 marks]
c.
reject (do not accept) \({{\text{H}}_0}\)\(\,\,\,\)OR\(\,\,\,\)accept \({{\text{H}}_1}\) (A1)(ft)
Note: Can be written in words.
\(19.0{\text{ }}(18.9640 \ldots ) > 12.6\) (R1) (C2)
Note: Accept “\(\chi _{calc}^2 > \chi _{crit}^2\)” for the (R1) provided their \(\chi _{calc}^2\) value is explicitly seen in their part (c).
OR
\((p = ){\text{ }}0.00422{\text{ }} < {\text{(significance level = ) }}0.05\) (R1) (C2)
Note: Do not award (R0)(A1)(ft). Follow through from part (c). Numerical comparison must be seen to award the (R1).
[2 marks]
d.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.
Syllabus sections
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