AS/A2 Stats 1 Stats 2

S3 Topic 4: Goodness of fit and contingency tables
Fitting a continuous Uniform distribution
Enter some figures (each should be greater than 5 but definitely bigger than 1) for Observed data in the top row of this table. This data will correspond to the classes shown above them, ie., 0-10, 10-20, and so on. An estimate of the mean will be then found, together with the Expected data and the calculation of S[O-E]²/E. H0: The Uniform distribution is a suitable model for the observed data H1: The Uniform distribution is not a suitable model for the observed data If S[O-E]²/E is greater than 14.067 then you can be 95% certain that your Observed data is not, in fact, from a continuous Uniform distribution.

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	70-80	80-90
Observed data
mean =
Expected data
[O-E]²/E =
S[O-E]²/E =

Summary Note that the above example is not typical. Often the classes used will not all be of equal width. If the classes span the range 0 to 90 say, then an individual class 10-12, will imply that there is a probability of 12/90 of a random variable occuring in that class. © MathsNet 2001