Step 1 :We are testing \(H_0:p=0.76\) versus \(H_\text{a} : p>0.76\), where \(p\) is the true proportion of residents that favor annexation.
Step 2 :First, we need to calculate the test statistic and the corresponding P-value. These values are not given in the problem.
Step 3 :Assuming that these values have been calculated and the conditions for inference were met, we can proceed to the conclusion step.
Step 4 :The P-value in this problem would be compared to the significance level \(\alpha=0.01\).
Step 5 :If the P-value is less than \(\alpha\), we would reject \(H_0\) and accept \(H_\text{a}\), concluding that there is sufficient evidence to support the claim that the percentage of residents who favor annexation is more than \(76 \%\).
Step 6 :If the P-value is greater than or equal to \(\alpha\), we would fail to reject \(H_0\), concluding that there is not sufficient evidence to support the claim that the percentage of residents who favor annexation is more than \(76 \%\).
Step 7 :Without the exact P-value, we cannot definitively answer this question. However, the process would follow these steps.