#### Answer

a)Null hypothesis: 0.5 is the ratio of adults in favour of death penalty. Alternative hypothesis: the ratio of adults in favour of death penalty is more than 0.5.
b)z=6.33
c)0.0000000001263996, there is sufficient evidence to support that the ratio of adults in favour of death penalty is more than 0.5.

#### Work Step by Step

a) The null hypothesis says that 0.5 is the ratio of adults in favour of death penalty. The alternative hypothesis says that the ratio of adults in favour of death penalty is more than 0.5.
b)The test statistic is:$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.64-0.5}{\sqrt{0.5(1-0.5)/511}}=6.33.$
c)$P=1.263996E-10=1.263996\cdot10^{-10}=0.0000000001263996$, which is really close to 0, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the ratio of adults in favour of death penalty is more than 0.5.