Question

Consider the observed frequency distribution for the set of random variables.

a. Perform a​ chi-square test using alpha=0.05 to determine if the observed frequencies follow the binomial probability distribution when p=0.50 and n=4.

b. Determine the​ p-value and interpret its meaning.

Random Variable, X	Frequency, Fo
0	29
1	96
2	151
3	96
4	28

Total 400

The​ chi-square test statistic is chi squared, χ2=______

p-value=______

Answer 1

X	Oi	Ei	(Oi - Ei)^2/Ei
0	29	25	0.6400
1	96	100	0.1600
2	151	150	0.0067
3	96	100	0.1600
4	28	25	0.3600
	400		1.3267

Ei = P(X = xi) * 400

P(X = x) = 4Cx * 0.5^x * (1-0.5)^(4 - x)

chi-square = 1.3267

p-value = 0.8568