Determine

(a) the chi squared2 test statistic,

(b) the degrees of freedom,

(c) the critical value using alpha equals 0.05=0.05, and

(d) test the hypothesis at the alpha equals 0.05=0.05 level of significance.

OutcomeABCD

Observed4242373742423939

Expected4040404040404040

H0: PA=PB=PC=PD =1/4

H1: At least one of the proportions is different from the others.

2) Determine

(a) the chi squared2 test statistic,

(b) the degrees of freedom,

(c) the critical value using alpha equals 0.05=0.05, and

(d) test the hypothesis at the alpha equals 0.05=0.05 level of significance.

X 0 1 2 3 4

Observed137121441389

Expected1.6 25.3 151.9405.1405.1

H0: The random variable X is binomial with n=4, p=0.8

H1: The random variable X is not binomial with n=4, p=0.8