| Exam Board | OCR |
|---|---|
| Module | Further Statistics AS (Further Statistics AS) |
| Session | Specimen |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Chi-squared test of independence |
| Type | Standard 2×2 contingency table |
| Difficulty | Standard +0.3 This is a standard chi-squared test for independence with a 2×2 contingency table. While it requires proper hypothesis setup, calculation of expected frequencies, test statistic, and conclusion, it follows a routine procedure taught in Further Statistics with no conceptual complications or novel problem-solving required. The 8 marks reflect method marks rather than difficulty, making it slightly easier than average. |
| Spec | 5.06a Chi-squared: contingency tables |
| Black | Non-black | |
| Men | 69 | 71 |
| Women | 30 | 55 |
| Answer | Marks |
|---|---|
| 3 | H :gender and car colour not associated |
| Answer | Marks |
|---|---|
| gender and car colour | B1 |
| Answer | Marks |
|---|---|
| [8] | 2.5 |
| Answer | Marks |
|---|---|
| 2.2b | Hypotheses correctly stated |
| Answer | Marks |
|---|---|
| context, acknowledge uncertainty | Yates’ Correction omitted |
| Answer | Marks | Guidance |
|---|---|---|
| 61.6 | 78.4 | 140 |
| 37.4 | 47.6 | 85 |
Question 3:
3 | H :gender and car colour not associated
0
H :gender and car colour associated
1
61.6 78.4 140
37.4 47.6 85
99 126
(cid:167) 1 1 1 1 (cid:183)
(cid:70) 1 2 (cid:32)6.92 (cid:168) (cid:169)61.6 (cid:14) 78.4 (cid:14) 37.4 (cid:14) 47.6 (cid:184) (cid:185)
(cid:62)(cid:32)0.773(cid:14)0.607(cid:14)1.273(cid:14)1.000(cid:64) (cid:32)3.653
(cid:31)3.841
Do not reject H
0
Insufficient evidence of a relationship between
gender and car colour | B1
M1
A1
M1
A1
A1FT
c
eM1
A1FT
[8] | 2.5
1.1
1.1
3.3
3.4
i1.1
1.1
2.2b | Hypotheses correctly stated
(allow “independent”)
Correct method for finding E
f
All E correct
f
n
Attempt at calculation of(cid:70)2,
e
allow even if no Yates’
mCorrection
Correct value of (cid:70)2, in range
[3.65, 3.66]
FT Compare their (cid:70)2explicitly
with 3.841
Correct first conclusion
Correctly interpreted, need
context, acknowledge uncertainty | Yates’ Correction omitted
(4.202), reject: can get
B1M1A1M1A0A1M1A1 (cid:32)7/8
FT their 3.653, but not their 3.841
61.6 | 78.4 | 140
37.4 | 47.6 | 85
3
n
e
m
i
c
e
p
SCarl believes that the proportions of men and women who own black cars are different. He obtained a random sample of people who each owned exactly one car. The results are summarised in the table below.
\begin{tabular}{|c|c|c|}
\hline
& Black & Non-black \\
\hline
Men & 69 & 71 \\
\hline
Women & 30 & 55 \\
\hline
\end{tabular}
Test at the 5\% significance level whether Carl's belief is justified. [8]
\hfill \mbox{\textit{OCR Further Statistics AS Q3 [8]}}