Your Practice Set – Applications and Interpretation for IBDP Mathematics
3 . The following table shows the inner diameters of 60 plastic tubes produced in a factory :
Inner diameter ( mm ) d � 10 10 �d
� 12 12 �d
� 14 d � 14 Frequency 7 16 22 15
A
2
� goodness of fit test is conducted at a 5 % significance level to determine whether the data can be modelled by Normal distribution with parameters N ( 13 , 4 ) .
( a ) |
Write down the null hypothesis of the test . |
|
|
[ 1 ] |
( b ) |
( i ) |
Write down the value of the expected frequency of the category “ d � 10
”.
|
( ii ) Hence , write down the degree of freedom of the test .
( c ) Find the p -value .
( d ) State the conclusion of the test with a reason .
[ 2 ]
[ 2 ]
[ 2 ]
4 . |
The following table shows the weights of 300 cats living in a castle : |
Weight ( kg ) |
w �
3
|
3
�w �
3.5
|
3.5
�w �
4
|
w �
4
|
Frequency |
49 |
131 |
83 |
37 |
A
2
� goodness of fit test is conducted at a 1 % significance level to determine whether the data can be modelled by Normal distribution with parameters N ( 3.4 , 0.15 ) .
( a ) Write down the null hypothesis of the test .
( b ) Write down the value of the expected frequency of the category “ w � 4 ”.
( c ) Write down the degree of freedom of the test .
( d ) Find the p -value .
( e ) State the conclusion of the test with a reason .
[ 1 ]
[ 1 ]
[ 1 ]
[ 2 ]
[ 2 ]
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