OCR MEI Further Statistics A AS Specimen — Question 3 10 marks

Exam BoardOCR MEI
ModuleFurther Statistics A AS (Further Statistics A AS)
SessionSpecimen
Marks10
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Mark schemeDownload PDF ↗
TopicChi-squared test of independence
TypeStandard 2×2 contingency table
DifficultyStandard +0.3 This is a standard chi-squared test of independence with a 2×2 contingency table requiring calculation of expected frequencies, test statistic, and comparison to critical value. While it requires showing detailed working and understanding of hypothesis testing procedure, it follows a completely routine template with no conceptual challenges beyond applying the standard formula. Slightly easier than average due to small table size and straightforward setup.
Spec5.06a Chi-squared: contingency tables
3 In this question you must show detailed reasoning. A student is investigating what people think about organic food. She wishes to see if there is any difference between the opinions of females and males. She takes a random sample of 100 people and asks each of them if they think that organic food is better for their health than non-organic food. She will use the data to conduct a hypothesis test. The table below shows the opinions of these 100 people.
\cline { 3 - 4 } \multicolumn{2}{c|}{}Sex
\cline { 3 - 4 } \multicolumn{2}{c|}{}FemaleMale
\multirow{2}{*}{
Opinion on
organic food
}		Organic better3518
\cline { 2 - 4 }Not better2225
  1. Explain why the student should use a random sample.
  2. Carry out a test at the \(5 \%\) significance level to examine whether there is any association between a person's sex and their opinion on organic food. Show your calculations.
Question 3:
AnswerMarks Guidance
3(i) A random sample enables proper inference about the
population to be undertaken.B2
[2]2.4
2.4B2 for correct explanation as
shown in answer column
OR
B1 for Npartially correct
explanation e.g. a random sample
is less likely to be biased
AnswerMarks Guidance
3(ii) DR
H : no association between sex and opinion on health
0
benefits of organic food
H : some association between sex and opinion on
1
health benefits of organic food
Expected frequency Female Male
Organic better 30.21 22.79
Not better 26.79 20.21
Contribution Female Male
Organic better 0.7595 1.0068
Not better 0.8564 1.1353
(cid:70)2 (cid:32)3.76
E
Refer to (cid:70)2 P
1
Critical value at 5% level = 3.84
3.76 < 3.84
S
Result is not significant
There is not enough evidence to suggest that there is
association between sex and opinion on health benefits
AnswerMarks
of organic food.B1
M1
A1
B1
C
B1
B1
B1
E1
AnswerMarks
[8]3.3
3.4
1.1
1.1
I
1.1
2.5
2.2b
AnswerMarks
3.5aAllow hypotheses and conclusion
in terms of independence.
N
For expected frequencies
E
M
Expected
NB This B1 mark cannot be
implied by a correct final value of
(cid:70)2
Yates correction not expected – if
used,
(cid:70)2 (cid:32)3.01 .
Degrees of freedom = 1
NB if H H reversed, or
0 1
‘correlation’ mentioned, do not
award first B1 and do not award
final E1
AnswerMarks Guidance
Expected frequencyFemale Male
Organic better30.21 22.79
Not better26.79 20.21
ContributionFemale Male
Organic better0.7595 1.0068
Not better0.8564 1.1353
33 3
AnswerMarks Guidance
3(i)0 2
02
AnswerMarks Guidance
3(ii)3 2 
Question 3:
3 | (i) | A random sample enables proper inference about the
population to be undertaken. | B2
[2] | 2.4
2.4 | B2 for correct explanation as
shown in answer column
OR
B1 for Npartially correct
explanation e.g. a random sample
is less likely to be biased
3 | (ii) | DR
H : no association between sex and opinion on health
0
benefits of organic food
H : some association between sex and opinion on
1
health benefits of organic food
Expected frequency Female Male
Organic better 30.21 22.79
Not better 26.79 20.21
Contribution Female Male
Organic better 0.7595 1.0068
Not better 0.8564 1.1353
(cid:70)2 (cid:32)3.76
E
Refer to (cid:70)2 P
1
Critical value at 5% level = 3.84
3.76 < 3.84
S
Result is not significant
There is not enough evidence to suggest that there is
association between sex and opinion on health benefits
of organic food. | B1
M1
A1
B1
C
B1
B1
B1
E1
[8] | 3.3
3.4
1.1
1.1
I
1.1
2.5
2.2b
3.5a | Allow hypotheses and conclusion
in terms of independence.
N
For expected frequencies
E
M
Expected
NB This B1 mark cannot be
implied by a correct final value of
(cid:70)2
Yates correction not expected – if
used,
(cid:70)2 (cid:32)3.01 .
Degrees of freedom = 1
NB if H H reversed, or
0 1
‘correlation’ mentioned, do not
award first B1 and do not award
final E1
Expected frequency | Female | Male
Organic better | 30.21 | 22.79
Not better | 26.79 | 20.21
Contribution | Female | Male
Organic better | 0.7595 | 1.0068
Not better | 0.8564 | 1.1353
3 | 3 | 3 | 3 | 4 | 5 | 6
--- 3(i) ---
3(i) | 0 | 2 | 0 | E
0 | 2
--- 3(ii) ---
3(ii) | 3 | 2 | 0 | 3 | 8
3 In this question you must show detailed reasoning.
A student is investigating what people think about organic food. She wishes to see if there is any difference between the opinions of females and males. She takes a random sample of 100 people and asks each of them if they think that organic food is better for their health than non-organic food. She will use the data to conduct a hypothesis test. The table below shows the opinions of these 100 people.

\begin{center}
\begin{tabular}{ | l | l | l | l | }
\cline { 3 - 4 }
\multicolumn{2}{c|}{} & Sex &  \\
\cline { 3 - 4 }
\multicolumn{2}{c|}{} & Female & Male \\
\hline
\multirow{2}{*}{\begin{tabular}{ l }
Opinion on \\
organic food \\
\end{tabular}} & Organic better & 35 & 18 \\
\cline { 2 - 4 }
 & Not better & 22 & 25 \\
\hline
\end{tabular}
\end{center}

(i) Explain why the student should use a random sample.\\
(ii) Carry out a test at the $5 \%$ significance level to examine whether there is any association between a person's sex and their opinion on organic food. Show your calculations.

\hfill \mbox{\textit{OCR MEI Further Statistics A AS  Q3 [10]}}
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