Question

In: Statistics and Probability

Five states were randomly selected and their members in the State or Federal parliament are noted...

Five states were randomly selected and their members in the State or Federal parliament are noted below. APC: 33, 10, 14, 12, 10; PDP: 19, 15, 10, 20, 20. At α=0.10, can it be concluded that there is a dependent relationship between the state and the political party affiliation of their representatives? Choose ALL the relevant options

Solutions

Expert Solution

Claim : There is a dependent relationship between the state and the political party affiliation of their representatives.

Hypothesis :  

H0: There is a not dependent relationship between the state and
      the political party affiliation of their representatives.

H1: There is a dependent relationship between the state and
the political party affiliation of their representatives.

Given values are observed frequency .

1 2 3 4 5 Total
APC 33 10 14 12 10 79
PDP 19 15 10 20 20 84
Total 52 25 24 32 30 163

Form the observed frequency find expected frequency .

Expected frequency =( row total * column total ) / Grand Total .

1 2 3 4 5
APC (79*52)/163=25.20 (79*25)/163=12.12 (79*24)/163=11.63 (79*32)/163=15.51 (79*30)/30=14.54
PDP (84*52)/163=26.80 (84*25)/163=12.88 (84*24)/163=12.37 (84*32)/163=16.49 (84*30)/163=15.46

Formula for test statistics :

    where Oi = observed frequency , Ei = expected frequency .

So here , test statistics = .

Find critical value : Df = ( # of row -1) (# of column -1) =(2-1) (5-1)=1*4=4

                               and here use level of significance = 0.05 .

                               Since critical value = 2.776

Decision : Test statistics value =    > critical value =2.776 ; since reject H0.

Conclusion : At 5% level of significance , is is sufficient eveidence to conclude that there is a
                dependent relationship between the state and the political party affiliation of their
                representatives.

orchestra answered 1 year ago
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