Question

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

Random Variable, X	Frequency, Fo
0	29
1	96
2	151
3	96
4	28
Total	400

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.

The​ chi-square test statistic is

chi squared, χ2=______

p-value=______

Answer 1

We can use the chi square test to test the null Hypothesis that data comes from a specific distribution.

H0: The observed frequencies follow the binomial probability distribution when p=0.50 and n=4

H1: the observed frequencies not follow the binomial probability distribution when p=0.50 and n=4

We know that the Binomial Distribution

Calculate Expected Proportion and Expected Frequencies

Random Variable X	Expected Proportion	Expected Frequency
0	=0.0625	0.0625*400 = 25
1	=0.25	0.25*400 = 100
2	=0.375	0.375*400 = 150
3	=0.25	0.25*400 = 100
4	=0.0625	0.0625*400 = 25