Final answer:
The null hypothesis represents the claim that the candidate is not favored by more than half of the voters, while the alternative hypothesis represents the claim that the candidate is favored by more than half of the voters. A decision that fails to reject the null hypothesis means there is not enough evidence to support the claim that the candidate is favored by more than half of the voters. The conclusion should state that there is not sufficient evidence to reject the null hypothesis.
Step-by-step explanation:
The null hypothesis, denoted as H0, represents the claim that the candidate is not favored by more than half of the voters. In this case, the null hypothesis would be that less than or equal to 50% of the voters favor the candidate. The alternative hypothesis, denoted as Ha, represents the claim that the candidate is favored by more than half of the voters. Therefore, the alternative hypothesis would be that more than 50% of the voters favor the candidate.
The random variable, denoted as P', represents the proportion of voters in the state who favor the candidate. The test statistic is calculated using the sample data and is used to make a decision about the null hypothesis. The p-value, a probability value, is calculated based on the test statistic. It represents the likelihood of obtaining the sample data or more extreme data if the null hypothesis is true.
If the decision fails to reject the null hypothesis, it means that there is not enough evidence to support the claim that the candidate is favored by more than half of the voters. The conclusion should state that there is not sufficient evidence to reject the null hypothesis and therefore, it cannot be concluded that the candidate is favored by more than half of the voters.