20N.1.SL.TZ0.T_10

pestleMathematicsAISLPaper 120N· sl-4-11-expected-observed-hypotheses-chi-squared-gof-t-testsource ↗

On $90$ journeys to his office, Isaac noted whether or not it rained. He also recorded his journey time to the office, and classified each journey as short, medium or long.

Of the $90$ journeys to the office, there were $3$ short journeys when it rained, $22$ medium journeys when it rained, and $15$ long journeys when it rained. There were also $14$ short journeys when it did not rain.

Isaac carried out a $χ^{2}$ test at the $5 %$ level of significance on these data, looking at the weather and the types of journeys.

Write down $H_{0}$ , the null hypothesis for this test.

[1]

Find the expected number of short trips when it rained.

[3]

The $p$ -value for this test is $0.0206$ .

State the conclusion to Isaac’s test. Justify your reasoning.

[2]

Markscheme / solution

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

type of journey and whether it rained are independent (A1) (C1)

Note: Accept “there is no association” or “not dependent”. Do not accept “not related” or “not correlated”. Accept equivalent terms for ‘type of journey’.

[1 mark]

$\frac{17}{90} \times \frac{40}{90} \times 90$ OR $\frac{17 \times 40}{90}$ (A1)(M1)

Note: Award (A1) for $17$ or $40$ seen. Award (M1) for $\frac{17}{90} \times \frac{40}{90} \times 90$ OR $\frac{17 \times 40}{90}$ seen.

$7.56 (7.55555 \dots, \frac{68}{9})$ (A1) (C3)

[3 marks]

reject (do not accept) $H_{0}$ (A1)

type of journey and whether it rained are not independent (A1)

Note: Follow through from part (a) for their phrasing of the null hypothesis.

$0.0206 < 0.05$ (R1) (C2)

Note: A comparison must be seen, either numerically or in words (e.g. $p$ -value < significance level). Do not award (R0)(A1).

[2 marks]

Examiners’ report

[N/A]