Question

the mayor of a town believes that more than 40% of the residents favor annexation of a new community. a sample of 800 voters showed that 43% of the residents favored annexation. is there sufficient evidence at the 0.02 level to support the mayor’s claim?
what is the alternative hypothesis for this test?
☐ $h_a: p \
eq 0.43$
☐ $h_a: \mu > 0.4$
☐ $h_a: p > 0.4$
☐ $h_a: \mu \
eq 0.4$

Explanation:

The mayor's claim is about the proportion (\(p\)) of residents favoring annexation being more than 40% (0.4). The alternative hypothesis (\(H_a\)) should reflect this claim. We use \(p\) (proportion) not \(\mu\) (mean) here. So \(H_a: p > 0.4\) matches the claim that more than 40% favor annexation.

Answer:

\(H_a: p > 0.4\)