Question

a candidate for governor of a certain state claims to be favored by at least half of the voters. if a hypothesis is formed, how should you interpret a decision that fails to reject the null hypothesis?
a. there is sufficient evidence to reject the claim ( p geq 0.5 ).
b. there is not sufficient evidence to reject the claim ( p geq 0.5 ).
c. there is not sufficient evidence to support the claim ( p geq 0.5 ).
d. there is sufficient evidence to support the claim ( p geq 0.5 ).

Explanation:

When we fail to reject the null hypothesis in a hypothesis - testing scenario, it means that the sample data does not provide enough evidence to go against the null hypothesis. In this case, the claim is \(p\geq0.5\) (where \(p\) is the proportion of voters favoring the candidate). Failing to reject the null hypothesis implies that we do not have sufficient evidence to reject the claim \(p\geq0.5\).

Answer:

B. There is not sufficient evidence to reject the claim \(p\geq0.5\).