Testing a Distribution for Goodness of Fits to Data
Given a set of data, we may suspect intuitively that it may be modelled by a particular model for intuitive reasons, because inspection of the data seems to imply it, or because a particular distribution , if it did fit the data, would be very convenient. Wedemonstrate how to test a distribution for goodness of fit to a setof data using thedistribution.
Suppose we have a list of data. The data represents the number of goals scored in a football tournament is illustrated in the table.
It is proposed to fit adistribution to this table. Conduct a hypothesis test.at the 10% level.
We complete the table below, using the fact that for a Poisson distribution with 100 observations and
We group together the last two columns since the last column has frequency less than 5.
Number of Goals, k  0  1  2  3  4  5  More than 5  5 or More 
Observed, O(k)  47  20  15  8  5  5  0  5 
Expected, E(k)  30.1  36,1  21.7  8.7  2.6  0.6  3.5  4.1 
O(k)E(k)  16.9  16.1  6.7  0.7  2.4  4.4  3.5  0.9 
\[(O(k)E(k))^2\]  285.61  259.21  44.89  0.49  5.76 

 0.81 
9.5  7.2  2.1  0.1  2.21 

 2.0 
There are 5 degrees of freedom. Referring to the