Apps. and Interpretation for IBDP Maths Ebook 2 | Page 295

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Solution
( a )
( i )
H
0 :
�d �
0
A1
( ii ) H
1
: �d
� 0 A1
( b ) p-value � 0.0225860627 ( A1 ) for correct value p-value � 0.0226 A1
( c ) � 2.43 A1
( d )
The null hypothesis is rejected .
A1
As p-value � 0.05
.
A1
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Exercise 77
1 . The table below shows the typing speed ( words per minute ) of a group of 7 students in a vocational training school before and after training :
Student
A
B
C
D
E
F
G
Typing speed before training
37
31
35
42
18
15
26
( x words per minute )
Typing speed after training ( y words per minute )
33
49
59
42
34
25
42

19

The curriculum development officer of the school wants to investigate whether on average the students show improvement after training . A paired t -test is conducted at a 1 % significance level . Define d �x � y .
( a )
Write down the alternative hypothesis of the test .
( b )
Find the p -value.
( c )
Write down the value of t , the test statistic .
( d )
State the conclusion of the test with a reason .
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[ 2 ] www . seprodstore . com
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