Problem

The mayor of a town has proposed a plan for the annexation of a new community. A political study took a sample of 800 voters in the town and found that $80 \%$ of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is more than $76 \%$. Testing at the 0.01 level, is there enough evidence to support the strategist's claim? Step 7 of 7 : State the conclusion of the hypothesis test. Answer 2 Points Keypad Keyboard Shortcuts There is sufficient evidence to support the claim that the percentage of residents who favor annexation is more than $76 \%$. There is not sufficient evidence to support the claim that the percentage of residents who favor annexation is more than $76 \%$.

Solution

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.

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Source: https://solvelyapp.com/problems/kxXJonrlzu/

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