You can use a goodness-of-fit test to determine whether all of the criteria for a binomial experiment have actually been met in a given application. Suppose that an experiment consisting of four trials was repeated 100 times. The number of repetitions on which a given number of successes was obtained is recorded in the table:

Estimate p (assuming that the experiment was binomial), obtain estimates of the expected cell frequencies, and test for goodness-of-fit. To determine the appropriate number of degrees of freedom for X2, note that p was estimated by a linear combination of the observed frequencies.

Possible Results (number of successes) Number of Times Obtained 17 42 21