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Date November 2016 Marks available 2 Reference code 16N.1.sl.TZ0.6
Level SL only Paper 1 Time zone TZ0
Command term Write down 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 χ2-test was performed at the 5% significance level.

The critical value for this test is 7.815.

The null hypothesis for the test is

H0: 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 χ2 statistic.

[2]
b.

State, giving a reason, whether the null hypothesis should be rejected.

[2]
c.

Markscheme

1001000×3301000×1000 OR 100×3301000     (M1)

=33     (A1)     (C2)

[2 marks]

a.

8.21 (8.21497…)     (A2)     (C2)

[2 marks]

b.

H0 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 H0 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 H0OR “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 χ2 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

Topic 4 - Statistical applications » 4.4
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