Concluding Tests Population Proportion Practice Test

A state agency wants to determine whether fewer than 15% of registered voters in the state are unaffiliated with any political party. In a random sample of 800 registered voters, 103 were unaffiliated. A one-sample $z$ test for a population proportion was performed with $H_0: p=0.15$ and $H_a: p<0.15$ at $\alpha=0.05$. The $p$-value was 0.041, so the agency rejected $H_0$. Which conclusion is appropriate?

A city council wants to know whether a majority of residents support building a new public library. A random sample of 200 residents found that 118 support the plan. A one-proportion $z$ test was conducted for $H_0: p=0.50$ versus $H_a: p>0.50$ at significance level $\alpha=0.05$. The test produced a $p$-value of 0.028, so the council rejected $H_0$. Which conclusion is appropriate?