Answer
There is sufficient evidence to support that the majority of adults feel vulnerable to identity theft.
Work Step by Step
$H_{0}:p=50$%=0.5. $H_{a}:p>0.5$ $\hat{p}$ is the number of objects with a specified value divided by the sample size. Hence $\hat{p}=\frac{x}{n}=\frac{521}{1002}=0.5299.$ The test statistic is:$z=\frac{\hat{p}-p}{\sqrt{p(1-p)/n}}=\frac{0.5299-0.5}{\sqrt{0.5(1-0.5)/1002}}=1.89.$ The P is the probability of the z-score being more than 1.89 which is 1 minus the probability of the z-score being less than1.89, hence:P=1-0.9706=0.0294. If the P-value is less than $\alpha$, which is the significance level, then this means the rejection of the null hypothesis. Hence:P=0.0294 is less than $\alpha=0.05$, hence we reject the null hypothesis. Hence we can say that there is sufficient evidence to support that the majority of adults feel vulnerable to identity theft.
