Apps. and Interpretation for IBDP Maths Ebook 2 | Page 356

Your Practice Set – Applications and Interpretation for IBDP Mathematics
75.3
( a )
H
0
: The data follows a
Normal distribution with
parameters N ( 13 , 4 ) .
( b )
( i )
4.01
( ii )
2
( c )
p-value �
0.407
( d )
The null hypothesis is not
rejected as p-value � 0.05
.
75.4
( a )
H
0
: The data follows a
Normal distribution with parameters N ( 3.4 , 0.15 ) .
( b )
18.2
( c )
3
( d )
p-value �
0.0000376
( e ) The null hypothesis is rejected as p-value � 0.01.
Exercise 76
76.1 ( a ) ( i ) H
0
: � � 17
( ii ) H
1
: � � 17 ( b ) p-value � 0.0456
( c ) The null hypothesis is rejected as p-value � 0.05.
76.2 ( a ) ( i ) H
0
: � � 28
( ii ) H
1
: � � 28 ( b ) p-value � 0.412
( c ) The null hypothesis is not rejected as p-value � 0.1.
76.3 ( a ) ( i ) H
0
: � � 7
( ii )
H
1 : � �
7
( b )
( i )
7.1875
( ii )
z �
0.433
( c )
The null hypothesis is not
rejected as z � 1.645
.
76.4
( a )
( i )
H
0 : � �
100
( ii )
H
1 : � �
100
( b )
( i )
106
( ii )
z �
5.55
( c )
The null hypothesis is
rejected as z � 2.326
.
Exercise 77
77.1
( a )
H
1 :
�d �
0
( b )
p-value �
0.0122
( c )
�
2.99
( d )
The null hypothesis is not
rejected as p-value �
0.01.
77.2
( a )
H
1 :
�d �
0
( b )
p-value �
0.133
( c )
1.21
( d )
The null hypothesis is not
rejected as p-value � 0.05
.
77.3 ( a ) ( i ) H
0
: �d
� 0
( ii ) H
1
: �d
� 0 ( b ) p-value � 0.222 ( c ) The null hypothesis is not rejected as p-value � 0.1.
( d )
4
9
77.4
( a )
( i )
H
0 : � �
0
( ii ) H
1
: �d
� 0 ( b ) p-value � 0.0198 ( c ) The null hypothesis is rejected as p-value � 0.05.
( d )
Exercise 78
2 3
78.1 ( a ) ( i ) H
0
: p � 0.15
( ii )
H
1 : p �
0.15
( b )
0.00426
( c )
The null hypothesis is
rejected as p-value �
0.01.
78.2
( a )
( i )
H
0 : � �
10
( ii )
H
1 : � �
10
( b )
0.208
( c )
The null hypothesis is not
rejected as p-value � 0.05
.
d
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