Exercise 75
1 . The following table shows the number of accidents on a highway in the last 120 days :
A
Number of accidents 0 1 2 3 4 or more Number of days 40 25 40 13 2
2
� goodness of fit test is conducted at a 10 % significance level to determine whether the data can be modelled by Poisson distribution with mean 2 .
( a ) Write down the null hypothesis of the test .
( b ) Write down the value of the expected frequency of the category “ 4 or more ”.
( c ) Write down the degree of freedom of the test .
2
( d ) Find the value of � calc
, the test statistic .
The critical value is given by 7.779 .
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( e ) State the conclusion of the test with a reason .
2 . The following table shows the number of goals conceded by a goalkeeper in 100 matches :
A
Number of goals conceded 0 1 2 3 4 5 Frequency 4 18 35 21 17 5
2
� goodness of fit test is conducted at a 5 % significance level to determine whether the data can be modelled by Binomial distribution with parameters B ( 5 , 0.4 ) .
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( a ) Write down the null hypothesis of the test .
( b ) ( i ) Write down the value of the expected frequency of the category “ 5 ”.
[ 1 ]
( ii ) Hence , write down the degree of freedom of the test .
2
( c ) Find the value of � calc
, the test statistic .
The critical value is given by 9.488 .
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( d ) State the conclusion of the test with a reason .
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