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2009
P2 Q10
Topical
Sampling
09 P2 Q10
2009 H2 Mathematics Paper 2 Question 10
Sampling Theory
Answers
(i)
Unbiased estimate of mean of
X
=
9.6
{X = 9.6}
X
=
9.6
Unbiased estimate of variance of
X
=
0.81
{X = 0.81}
X
=
0.81
(ii)
The Central Limit Theorem does not apply as the sample size
n
=
9
{n=9}
n
=
9
is not large enough
(iii)
Out of syllabus
Full solutions
(i)
Unbiased estimate of mean of
X
=
x
‾
=
∑
x
n
=
86.4
9
=
9.6
■
\begin{align*} & \textrm{Unbiased estimate of mean of } X \\ & = \overline{x} \\ & = \frac{\sum x}{n} \\ & = \frac{86.4}{9} \\ & = 9.6 \; \blacksquare \end{align*}
Unbiased estimate of mean of
X
=
x
=
n
∑
x
=
9
86.4
=
9.6
■
Unbiased estimate of variance of
X
=
s
2
=
1
n
−
1
(
∑
x
2
−
(
∑
x
)
2
n
)
=
1
9
−
1
(
835.92
−
(
86.4
)
2
9
)
=
0.81
■
\begin{align*} & \textrm{Unbiased estimate of variance of } X \\ & = s^2 \\ & = \frac{1}{n-1}\left( \sum x^2 - \frac{\left(\sum x\right)^2}{n} \right) \\ & = \frac{1}{9-1}\left( 835.92 - \frac{\left(86.4\right)^2}{9} \right) \\ & = 0.81 \; \blacksquare \end{align*}
Unbiased estimate of variance of
X
=
s
2
=
n
−
1
1
(
∑
x
2
−
n
(
∑
x
)
2
)
=
9
−
1
1
(
835.92
−
9
(
86.4
)
2
)
=
0.81
■
(ii)
The Central Limit Theorem does not apply as the sample size
n
=
9
{n=9}
n
=
9
is not large enough
(iii)
Out of syllabus
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