Question

the mayor of a town believes that under 56% of the residents favor annexation of a new bridge. 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 assumes the proportion $p$ is greater than or equal to the claimed value. So, $H_0:p\geq0.56$.

Step2: Define alternative hypothesis

The alternative hypothesis $H_a$ is what the mayor claims. The mayor believes that the proportion of residents who favor annexation is less than 56%, so $H_a:p < 0.56$.

Answer:

$H_0:p\geq0.56$
$H_a:p < 0.56$