14.46 Fitting a Binomial Distribution 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 bino- mial), obtain estimates of the expected cell frequen- cies, and test for goodness of fit. To determine the appropriate number of degrees of freedom for x, note that p was estimated by a linear combination of the observed frequencies.

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Possible Results (number of successes) 0 1 Number of Times Obtained 11 17 2 42 3 21 4 9