18N.1.SL.TZ0.T_4

pestleMathematicsAISLPaper 118N· sl-4-11-expected-observed-hypotheses-chi-squared-gof-t-testsource ↗

Abhinav carries out a χ² test at the 1 % significance level to determine whether a person’s gender impacts their chosen professional field: engineering, medicine or law.

He surveyed 220 people and the results are shown in the table.

State the null hypothesis, H₀, for this test.

[1]

Calculate the expected number of male engineers.

[2]

Find the p-value for this test.

[2]

Abhinav rejects H₀.

State a reason why Abhinav is incorrect in doing so.

[1]

Markscheme / solution

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

gender and chosen profession are independent (A1) (C1)

Note: Accept there is no association between chosen profession and gender. Accept “not dependent”. Do not accept “not related” or “not correlated” or “not influenced”, or “does not impact”.

[1 mark]

$\frac{{110}}{{220}} \times \frac{{90}}{{220}} \times 220$ $\left( {\frac{{110 \times 90}}{{220}}} \right)$ (M1)

Note: Award (M1) for correct substitution into expectation formula.

= 45 (A1) (C2)

[2 marks]

0.0193 (0.0192644…) (A2) (C2)

[2 marks]

0.0193 > 0.01 (1%) (A1)(ft)

the p-value is greater than the significance level (1%) (A1)(ft) (C1)

Note: A numerical value in (c) must be seen to award the (A1)(ft). Follow through from part (c), only if it is > 0.01.

Accept a correct answer from comparing both the numerical value of the Χ² statistic and the numerical value of the critical value: 7.89898… < 9.21.

[1 mark]

Examiners’ report

[N/A]