Statistics - Chi square/null and alt. hypothesis/decision rule?

[JARED]

The null hypothesis and the alternate are:

H0:The frequencies are equal.
H1:The frequencies are not equal.

Categoryf0
A 30
B 30
C 15
D 15

a) State the decision rule, using the 0.01 significance level. (Round your answer to 3 decimal places.)

Reject H0 if X2 > _______

b) Compute the value of chi-square. (Round your answer to 1 decimal place.)


X2 = _______


c) Reject or do not reject H0? The frequencies are equal or not equal?

 

[paramvenu]

Category --- A B C D
Observed f --- 30 30 15 15 Total = 90
Expected f --- 22.5 22.5 22.5 22.5 Total = 90
(Exp f = 90/4)
a) Degrees of freedom = n-1 = 4-1 = 3
Critical value of Chi-square for 3 d.f at alpha = 0.01 is 11.34
Reject Ho if Calculated Chi-square > 11.34 being the critical value
b) Chi-square = sigma {(O-E)^2/E}
= {(30-22.5)^2/22.5) + (30-22.5)^2/22.5) + (15-22.5)^2/22.5) + (15-22.5)^2/22.5)}
= {2.5+2.5+2.5+2.5}
= 10.0
c) Do not reject the Ho. The frequencies are equal in statistical terms.