| Date | November 2016 | Marks available | 2 | Reference code | 16N.1.sl.TZ0.6 |
| Level | SL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 6 | Adapted from | N/A |
Question
A hospital collected data from 1000 patients in four hospital wards to review the quality of its healthcare. The data, showing the number of patients who became infected during their stay in hospital, was recorded in the following table.
A \({\chi ^2}\)-test was performed at the 5% significance level.
The critical value for this test is 7.815.
The null hypothesis for the test is
\({{\text{H}}_0}\): Becoming infected during a stay in the hospital is independent of the ward.
Find the expected frequency of the patients who became infected whilst in Nightingale ward.
[2]
a.
For this test, write down the \({\chi ^2}\) statistic.
[2]
b.
State, giving a reason, whether the null hypothesis should be rejected.
[2]
c.
Markscheme
\(\frac{{100}}{{1000}} \times \frac{{330}}{{1000}} \times 1000\) OR \(\frac{{100 \times 330}}{{1000}}\) (M1)
\( = 33\) (A1) (C2)
[2 marks]
a.
8.21 (8.21497…) (A2) (C2)
[2 marks]
b.
\({{\text{H}}_0}\) should be rejected (A1)(ft)
\(7.815 < 8.21\) OR (the \(p\)-value) \(0.041771 < 0.05\) (R1) (C2)
Note: Follow through from part (b). Do not award (A1)(R0).
Award (A1)(ft) for “\({{\text{H}}_0}\) should be rejected” OR “Becoming infected during a stay in hospital is not independent of (is dependent on OR associated with) the ward”. Accept “Do not accept \({{\text{H}}_0}\)” OR “YES”. Do not accept “Becoming infected during a stay in hospital is correlated (related OR linked) with the ward.”
Award (R1) for comparison of their \({\chi ^2}\) statistic value from part (b) with the critical value OR a comparison of \(p\)-value with 0.05.
[2 marks]
c.
Examiners report
[N/A]
a.
[N/A]
b.
[N/A]
c.
Syllabus sections
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