Question

the mayor of a town believes that less than 57% of the residents favor annexation of a new community. is there sufficient evidence at the 0.01 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 assumes the proportion is greater than or equal to the claimed proportion.
$H_0:p\geq0.57$

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is the claim we are trying to find evidence for. The mayor believes less than 57% favor annexation.
$H_a:p < 0.57$

Answer:

$H_0:p\geq0.57$
$H_a:p < 0.57$