Question

the mayor of a town believes that above 72% of the residents favor annexation of an adjoining community. is there sufficient evidence at the 0.05 level to support the mayors claim? state the null and alternative hypotheses for the above scenario.

Explanation:

Step1: Define null hypothesis

The null hypothesis ($H_0$) is a statement of no - effect or no difference. Here, it will be the opposite of the mayor's claim. So, $H_0$ assumes that the proportion of residents who favor annexation is less than or equal to 72%.
$H_0: p\leq0.72$

Step2: Define alternative hypothesis

The alternative hypothesis ($H_a$) is what we are trying to find evidence for. The mayor believes that more than 72% of the residents favor annexation. So, $H_a$ is $p > 0.72$.
$H_a: p>0.72$

Answer:

$H_0: p\leq0.72$
$H_a: p > 0.72$