Question

Two sample of votes for two candidates A and B for a public officer are taken one from among the residents of rural areas the results are given in the adjoining table examine whether the nature of the area is related to voting preference in this election

Answer 1

$H_0:$ the nature of the area is not related to voting preference in this election.

$H_1:$ the nature of the area is related to voting preference in this election.

Sample size $n=100.$

$\alpha=0.05$

We will use $\chi^2$ test.

We have the contingency table $2\times 2$ with the observed values.

We calculate the expected values:

Expected value (A, Rural)$=56\cdot\frac{39}{100}=21.84$.

Expected value (A, Urban)$=56\cdot\frac{61}{100}=34.16$.

Expected value (B, Rural)$=44\cdot\frac{39}{100}=17.16.$

Expected value (B, Urban)$=44\cdot\frac{61}{100}=26.84.$

$\chi^2_{obs}=\sum\frac{(O_i-E_i)^2}{E_i}\approx 0.58$.

Using CHISQ.DIST.RT ($\chi^2_{obs};df$) in Excel we find $p-value\approx 0.45.$

$df=(2-1)(2-1)=1.$

$p-value>\alpha.$ So we accept $H_0:$ the nature of the area is not related to voting preference in this election.