A random sample of n observations,each of which could be classified into exactly one of k categories,is selected.Suppose that a null hypothesis specifies category probabilities that depend on the estimation of m unknown population parameters.How many degrees of freedom does a goodness-of-fit-test have when population parameters are estimated?
A)k - 1
B)m - 1
C)k - m - 1
D)k + m - 1

Question

Quizplus · Accepted Answer

In a goodness-of-fit test, we are testing whether the observed data follows a specified distribution. The null hypothesis specifies category probabilities that depend on the estimation of m unknown population parameters, which means that we need to estimate these parameters from the sample data in order to test the null hypothesis.

The number of degrees of freedom in a goodness-of-fit test is equal to the number of categories (k) minus the number of parameters that need to be estimated (m). This is because once we estimate m parameters, we lose m degrees of freedom.

Therefore, the correct formula is: df = k - m.

Hence, the answer is (C) k - m - 1.

A Random Sample of N Observations,each of Which Could Be