There was a wonderful study conducted in 1898 by von Bortkiewicz,which provides data on the death of soldiers in the Prussian army from kicks by horses and mules.The data pertain to 10 army corps,each observed over 20 years,for a total of 200 corps-years.The following table summarizes the observed data.Note that 109 corps-years had 0 deaths and 65 corps-years had 1 death,etc. Von Bortkiewicz felt that a distribution known as the Poisson distribution would describe these data well.Using that distribution,he produced the following probabilities. Under the null hypothesis that the observed cell counts follow the specified distribution,what is the distribution of the test statistic?
A) with 5 degrees of freedom
B) with 1 degree of freedom
C) with 3 degrees of freedom
D) with 4 degrees of freedom
E)This cannot be determined without knowing its value.

Question

There was a wonderful study conducted in 1898 by von Bortkiewicz,which provides data on the death of soldiers in the Prussian army from kicks by horses and mules.The data pertain to 10 army corps,each observed over 20 years,for a total of 200 corps-years.The following table summarizes the observed data.Note that 109 corps-years had 0 deaths and 65 corps-years had 1 death,etc.  Von Bortkiewicz felt that a distribution known as the Poisson distribution would describe these data well.Using that distribution,he produced the following probabilities.  Under the null hypothesis that the observed cell counts follow the specified distribution,what is the distribution of the test statistic?
A) with 5 degrees of freedom 
B) with 1 degree of freedom 
C) with 3 degrees of freedom 
D) with 4 degrees of freedom 
E)This cannot be determined without knowing its value.

Quizplus · Accepted Answer

The test statistic used to test goodness of fit for Poisson distribution is chi-square distribution with k-1 degrees of freedom, where k is the number of cells. In this case, there are 10 cells, so the degrees of freedom is 10-1=9. However, since there is only one parameter estimated (the mean of the Poisson distribution), we lose one degree of freedom, giving us 9-1=8 degrees of freedom. Therefore, the distribution of the test statistic is a chi-square distribution with 8 degrees of freedom, so the best choice is D.

There Was a Wonderful Study Conducted in 1898 by Von