Question

Determine​ (a) the χ2 test​ statistic, (b) test degrees of​ freedom, (c) the critical value using α=0.05​, and​ (d) test the hypothesis at the α=0.05 level of significance. Outcome           Observed          Expected A          18         20 B          18         20 C          22         20 D          22         20

H0:Pa=Pb=Pc=Pd=1/4

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

(a)test statistics is 0.8

(b) There are 3 degrees of freedom

(c) The critical value is X ??

(round three decimal places as needed)

Please assist me in answering the critical value.

Answer 1

Solution :

Given that ,

degrees of freedom = 3

P( $\chi^2$ ₃ > 7.815) = 0.05

Critical value = 7.815