Question

Determine​ (a) the chi squaredχ2 test​ statistic, (b) the degrees of​ freedom, (c) the critical value using alpha equals 0.05α=0.05​, and​ (d) test the hypothesis at the alpha equals 0.05α=0.05 level of significance.		Outcome	A	B	C	D
		Observed	101101	9999	109109	9191
		Expected	100100	100100	100100	100100

Upper H 0H0​:

p Subscript Upper ApAequals=p Subscript Upper BpBequals=p Subscript Upper CpCequals=p Subscript Upper DpDequals=one fourth14

H1​:

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

​(a) The test statistic is

nothing.

​(Type an exact​ answer.)

Answer 1

(a) The test-statistic for the given testing problem is, = = + + + = = 1.64

Under H0, follows chi-square distribution with (4-1) = 3 d.f.

(b) The degrees of freedom is = 4-1 = 3.

(c) The critical value is = = 7.82.

(d) Since, observed < , we fail to reject the null hypothesis H0.