Question

a candidate for governor of a certain state claims to be favored by at least half of the voters. if a hypothesis test is performed, how should you interpret a decision that rejects the null hypothesis?

a. there is sufficient evidence to reject the claim $\
ho \geq 0.5$.
b. there is sufficient evidence to support the claim $\
ho \geq 0.5$.
c. there is not sufficient evidence to support the claim $\
ho \geq 0.5$.
d. there is not sufficient evidence to reject the claim $\
ho \geq 0.5$.

Explanation:

In hypothesis testing, the null hypothesis \(H_0\) is the statement being tested. Here, the claim is \(p\geq0.5\), so the null hypothesis \(H_0:p\geq0.5\). When we reject the null hypothesis, it means that the sample data provides enough evidence against the null hypothesis. That is, there is sufficient evidence to say that the null hypothesis is false.

Answer:

A. There is sufficient evidence to reject the claim \(p\geq0.5\).