Question

Determine if X follows a binomial distribution with 4 trials and p=0.5.

X (number of successes)	0	1	2	3	4
Frequency	24	17	23	10	34

Answer 1

X follows the binomial distribution

X does not follow binomial distribution

X (number of success)	Frequency	Binomial Probability	Expected frequency (nP(x))
0	24	0.0625	6.75
1	17	0.25	27
2	23	0.375	40.5
3	10	0.25	27
4	34	0.0625	6.75
Total	n=108

Test statistic:

the degree of freedom: 4-1=3

P value for the chi-square test is less than 0.0001

Since the P value is less than the significance level 0.05 of the test. We can reject the null hypothesis, hence we have no evidence that X follow the binomial distribution.