Step 1 :The null hypothesis is a statement of no effect or status quo. In this case, it would be that the proportion of subjects who respond in favor is equal to 0.5. The alternative hypothesis is what we are testing against the null hypothesis. In this case, it would be that the proportion of subjects who respond in favor is not equal to 0.5. So, the null and alternative hypotheses for this test are: \[\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p \neq 0.5 \end{array}\]
Step 2 :The test statistic can be calculated using the formula for a one-sample z-test for proportions, which is \((p_{hat} - p_0) / \sqrt{(p_0 * (1 - p_0)) / n}\), where \(p_{hat}\) is the sample proportion, \(p_0\) is the hypothesized population proportion, and n is the sample size.
Step 3 :Given that the number of adults in favor is 481, the number of adults opposed is 397, and the total number of adults is 878, we can calculate the sample proportion \(p_{hat}\) as 0.5478359908883826.
Step 4 :Substituting these values into the formula, we get the test statistic as approximately 2.83.
Step 5 :Final Answer: The null and alternative hypotheses for this test are: \[\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p \neq 0.5 \end{array}\] The test statistic for this hypothesis test is \(\boxed{2.83}\).