Apps. and Interpretation for IBDP Maths Ebook 2 | Page 359

Answers
( d )
( 1 )
6
( 2 )
1.54
( 3 )
The null hypothesis is not rejected as
2
�
� 14.449
.
calc
III ( e ) ( 1 ) H
0
: �d
� 0
( 2 )
H
1 :
�d �
0
( 3 )
p-value �
0.0584
( 4 ) The null hypothesis is rejected as p-value � 0.1.
( f )
( 1 )
The numbers of books sold by the two authors follow a bivariate normal distribution .
( 2 )
H
0 : � �
0
( 3 )
H
1 : � �
0
( 4 )
p-value �
0.0111
( 5 )
The null hypothesis is
rejected as p-value �
0.05.
( g )
( 1 )
(
� 0.592 , 20.0 )
Exercise 81
( 2 ) The above result is not consistent with the conclusion of the hypothesis test in ( e ) as 0 is included in the confidence interval .
81.1 ( a ) Refer to solution �4 12�
( b ) ( 1 ) M � � � �1 0 �
2 ( 2 ) � �4��
12 ( 3 ) �1 �� 2 , �2 � 6
��2� �6�
( 4 ) v
1
� � � , v
2
� � � � 1 � �1�
( 5 ) y � Ae � Be
�2x 6x
( 6 ) Refer to solution
( c )
( 1 )
The eigenvalues of
M are the solutions
2 of � � 4��12 �
0, where � 4 and
� 12 are the coefficients of dy and y in dx 2 d y dy � 4
�12y � 0
.
2 dx dx
( 2 )
( d ) ( 1 ) ( 2 )
2 d y dy
� b � cy � 0
2 dx dx y � Ae � Be
3x 9x y � e � e
3 9
2 x x
81.2
( a )
( 1 )
�
2
( 2 )
1
2
( 3 )
1
9 y� x� 2
2
( 4 )
� 19
� �10 ,
� � 2
�
( 5 )
559 m
( b )
( 1 )
333 m
( 2 )
6450 m
( c )
( 1 )
6
( 2 )
4
( d )
Eulerian circuit does not exist
as not all vertices are of even
degree .
( e )
( 1 )
CJ
( 2 )
CJ , HI , DE , FG , AB , BH , BC , AD and GH
( 3 )
265 s
( f )
EF , FG , GH , HB , BC , CB ,
BA , AD , DA , AG , GH , HI , IJ ,
JC , CD and DE
( g )
AD , BC , GH
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