Your Practice Set – Applications and Interpretation for IBDP Mathematics
75
Paper 1 – Goodness-Of-Fit Test
Example
In an experiment , an unbiased six-sided die with faces 0 , 1 , 2 , 3 , 4 and 5 is tossed for 100 times . The following table shows the frequencies of the outcomes :
Outcome 0 1 2 3 4 5 Frequency 6 15 22 29 13 15
A
2
� goodness of fit test is conducted at a 5 % significance level to determine whether the data can be modelled by Poisson distribution with mean 3 .
( a ) Write down the null hypothesis of the test .
( b ) ( i ) Write down the value of the expected frequency of the outcome “ 0 ”.
( 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 .
( d ) State the conclusion of the test with a reason .
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Solution
( a ) H
0
: The data follows a Poisson distribution with mean 3 .
( b ) ( i ) 4.97 A1
A1
( ii ) 4 A1
( c ) 3.52 A2
( d ) The null hypothesis is not rejected . A1
2
As � � 9.488 . A1 calc
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