Answer
There is sufficient evidence to reject the claim that the winning candidate got 43% of the votes.
Work Step by Step
$H_{0}:p=0.43$. $H_{a}:p\ne0.43.$ $\hat{p}$ is the number of objects with a specified value divided by the sample size. Hence $\hat{p}=\frac{x}{n}=\frac{308}{611}=0.5041.$ The test statistic is:$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.5041-0.43}{\sqrt{0.43(1-0.43)/611}}=3.7.$ The P is the probability of the z-score being more than 3.7 or less than -3.7 is the sum of the probability of the z-score being less than -3.7 plus 1 minus the probability of the z-score being less than 3.7, hence:P=0.0001+1-0.9999=0.0002. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P=0.0002 is less than $\alpha=0.1$, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to reject the claim that the winning candidate got 43% of the votes.
