A One-Sided Goodness-of-Fit Test for a Multinomial Population.

A sample is taken from a population consisting of g + 1 groups or classes with unknown probability p[sub j] that an individual chosen is from class j, j = 0 ..... g. The null hypothesis Ho: p[sub j] is greater than or equal to P[sub j](j = 1 ,..., g), implying that none of the classes 1,..., g is underrepresented, must be tested; P[sub j] is the known fraction of the population belonging to class j. A modification of the chi-squared goodness-of-fit test that takes into account the one-sided nature of the hypothesis is derived and illustrated. The test for overrepresentation is also given. The test for under-representation is important for equal opportunity cases, and the test for overrepresentation is important in food and drug testing. [ABSTRACT FROM AUTHOR]