17M.1.SL.TZ1.T_6

pestleMathematicsAISLPaper 117M· sl-4-11-expected-observed-hypotheses-chi-squared-gof-t-testsource ↗

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.

M17/5/MATSD/SP1/ENG/TZ1/06

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]

Write down the number of degrees of freedom for this test.

[1]

Use your graphic display calculator to find the ${\chi ^2}$ statistic for this test.

[2]

State the conclusion for this test. Give a reason for your answer.

[2]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

30 (A1) (C1)

[1 mark]

6 (A1) (C1)

[1 mark]

${\text{19.0 (18.9640)}} \ldots$ (A2)(ft) (C2)

Note: Follow through from part (a).

Award (A1) for truncation to 18.9.

[2 marks]

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).

$(p = ){\text{ }}0.00422{\text{ }} < {\text{(significance level = ) }}0.05$ (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]

Examiners’ report

[N/A]