Question

Outcome Observed Expected20 20 20 20 ABCD만 18 Determine a) the χ test statistic b the degrees of freedom, c the critical value using- 05, and d test the hypothesis at the a 0 5 level of significance. H, At least one of the proportions is different from the others a) The test statistic is Type an exact answer)

Answer 1

(a)

Chisquareteststatistic-2-((Observed- E.rpected) /E.rpected) served - xpecte

Thus Chi square test statistic = 0.2 + 0.05 + 0.05 + 0 = 0.3

(b)

The degrees of freedom = (n-1) , since n = 4 , degrees of freedom = 3

(c)

at alpha = 0.05 level of significance, the critical chi square at 3 degrees of freedom = 7.815

However since the test statistic = 0.3 < 7.815, we fail to reject the null hypothesis. In order words we fail to reject that p1 = p2 = p3 = p4 = 1/4