CAIE A-Level Further Math 4.3.3 Independence test
Practise testing independence in contingency tables by calculating expected frequencies, χ2 statistics and contextual conclusions.
- Syllabus
- 2028–2030
- Course
- Further Mathematics 9231
- Level
- AS
Practise testing independence in contingency tables by calculating expected frequencies, χ2 statistics and contextual conclusions.
A town council has published its plans for redeveloping the town centre and residents are being asked whether they approve or disapprove. A random sample of 250 responses has been selected from residents in the four main streets in the town: North, East, South and West Streets. The results are shown in the table.

Test, at the 5% significance level, whether the opinions of the residents are independent of the streets on which they live.
H0: opinion is independent of street H1: opinion is not independent of street
B1
33 & 32.24 & 54 & 57.66 & 42 & 43.4 & 26 & 21.7 & 155
19 & 19.76 & 39 & 35.34 & 28 & 26.6 & 9 & 13.3 & 95
52 & & 93 & & 70 & & 35 & & 250
M1
At least 2 correct values or expressions.
A1
6 correct values or expressions.
Calculate chi-squared values:
0.0179+0.2323+0.0452+0.8521+0.0292+0.3790+0.0737+1.3902
M1
Correct to 3 decimal places.
At least 2 correct values or expressions.
3.02
A1
SC B1 3.02 following M1M0
SC B2 3.02 following M0M0
Tabular value, 3 degrees of freedom 7.815: ' 3.02 ' <7.815, accept H0
M1
Allow 'not significant'.
Insufficient evidence to suggest that opinion depends on street.
A1
CWO. Correct conclusion in context, following correct
work, level of uncertainty in language.
A0 if hypotheses wrong way round or missing.
7