OCR MEI Further Statistics Minor 2020 November — Question 3 8 marks

Exam BoardOCR MEI
ModuleFurther Statistics Minor (Further Statistics Minor)
Year2020
SessionNovember
Marks8
PaperDownload PDF ↗
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 with critical value. While it requires showing detailed reasoning and multiple computational steps, it follows a completely routine procedure taught in Further Statistics with no conceptual challenges or novel insights needed.
Spec5.06a Chi-squared: contingency tables
3 In this question you must show detailed reasoning. In a survey into pet ownership, one of the questions was 'Do you own either a cat or a dog (or both)?'. A total of 121 people took part in the survey and you should assume that they form a random sample of people in a particular town. The results, classified by the age of the person being surveyed, are shown in Table 3. \begin{table}[h]
\multirow{2}{*}{}Ownership of cat or dog
Does ownDoes not own
\multirow{2}{*}{Age}Over 45 years3829
Under 45 years2331
\captionsetup{labelformat=empty} \caption{Table 3}
\end{table} Carry out a test at the 10\% significance level to investigate whether, for people in this town, there is any association between age and ownership of a cat or dog.
Question 3:
AnswerMarks
3DR
H : no association between age of person and
0
ownership
H : some association between age of person and
1
ownership
Expected Does own Does not
Over 45 33.78 33.22
Under 45 27.22 26.78
Contribution Does own Does not
0.5280 0.5368
Over 45
(0.5272) (0.5361)
0.6551 0.6661
Under 45
(0.6542) (0.6650)
X2 =2.386[2.38,2.39]
Refer to χ2
1
(Critical value at 10% level = 2.71);
2.386 < 2.71 Result is not significant oe
there is not enough evidence to suggest that there is
association between age (of person) and ownership (of
AnswerMarks
dogs or cats)B1
M1
A1
B1
B1
B1
M1
A1
AnswerMarks
[8]3.3
3.4
1.1
1.1
1.1
2.5
3.5a
AnswerMarks
2.2bFor both hypotheses correct
E values accurate to at least 1dp
Values must be seen or calculation
method clearly indicated; this mark
cannot be implied merely by a correct
final value of X 2
For 1 degree of freedom (may be
implied by correct c.v.)
For comparison of their t.s. with
correct c.v. and conclusion
Conclusion not too assertive and in
AnswerMarks
contextAllow hypotheses and
conclusion in terms of
independence, but if
‘correlation’ is
mentioned the first B1
and final A1 cannot be
earned
Yates’ correction is not
expected, but gains full
marks if used correctly
Does
Does not
own
0.4104 0.4172
o (0.4097) (0.4166)
0.5092 0.5177
u (0.5084) (0.5167)
X2 =1.85(awrt)
A0 if hypotheses are
reversed
AnswerMarks Guidance
ExpectedDoes own Does not
Over 4533.78 33.22
Under 4527.22 26.78
ContributionDoes own Does not
Over 450.5280 0.5368
(0.5272)(0.5361)
Under 450.6551 0.6661
(0.6542)(0.6650)
Does
Does not
own
AnswerMarks Guidance
o0.4104 0.4172
(0.4097)(0.4166)
u0.5092 0.5177
(0.5084)(0.5167) 
Question 3:
3 | DR
H : no association between age of person and
0
ownership
H : some association between age of person and
1
ownership
Expected Does own Does not
Over 45 33.78 33.22
Under 45 27.22 26.78
Contribution Does own Does not
0.5280 0.5368
Over 45
(0.5272) (0.5361)
0.6551 0.6661
Under 45
(0.6542) (0.6650)
X2 =2.386[2.38,2.39]
Refer to χ2
1
(Critical value at 10% level = 2.71);
2.386 < 2.71 Result is not significant oe
there is not enough evidence to suggest that there is
association between age (of person) and ownership (of
dogs or cats) | B1
M1
A1
B1
B1
B1
M1
A1
[8] | 3.3
3.4
1.1
1.1
1.1
2.5
3.5a
2.2b | For both hypotheses correct
E values accurate to at least 1dp
Values must be seen or calculation
method clearly indicated; this mark
cannot be implied merely by a correct
final value of X 2
For 1 degree of freedom (may be
implied by correct c.v.)
For comparison of their t.s. with
correct c.v. and conclusion
Conclusion not too assertive and in
context | Allow hypotheses and
conclusion in terms of
independence, but if
‘correlation’ is
mentioned the first B1
and final A1 cannot be
earned
Yates’ correction is not
expected, but gains full
marks if used correctly
Does
Does not
own
0.4104 0.4172
o (0.4097) (0.4166)
0.5092 0.5177
u (0.5084) (0.5167)
X2 =1.85(awrt)
A0 if hypotheses are
reversed
Expected | Does own | Does not
Over 45 | 33.78 | 33.22
Under 45 | 27.22 | 26.78
Contribution | Does own | Does not
Over 45 | 0.5280 | 0.5368
(0.5272) | (0.5361)
Under 45 | 0.6551 | 0.6661
(0.6542) | (0.6650)
Does
Does not
own
o | 0.4104 | 0.4172
(0.4097) | (0.4166)
u | 0.5092 | 0.5177
(0.5084) | (0.5167)
3 In this question you must show detailed reasoning.
In a survey into pet ownership, one of the questions was 'Do you own either a cat or a dog (or both)?'. A total of 121 people took part in the survey and you should assume that they form a random sample of people in a particular town. The results, classified by the age of the person being surveyed, are shown in Table 3.

\begin{table}[h]
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{\multirow{2}{*}{}} & \multicolumn{2}{|c|}{Ownership of cat or dog} \\
\hline
 &  & Does own & Does not own \\
\hline
\multirow{2}{*}{Age} & Over 45 years & 38 & 29 \\
\hline
 & Under 45 years & 23 & 31 \\
\hline
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Table 3}
\end{center}
\end{table}

Carry out a test at the 10\% significance level to investigate whether, for people in this town, there is any association between age and ownership of a cat or dog.

\hfill \mbox{\textit{OCR MEI Further Statistics Minor 2020 Q3 [8]}}
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