Final answer:
The student is asked to use hypothesis testing to evaluate a Republican governor's reelection chances based on a survey. A null hypothesis would be established based on the historical requirement of 80% support in northern regions. A statistical z-test would then be used to determine if the governor's actual survey result significantly deviates from this benchmark.
Step-by-step explanation:
To assess the Republican governor's chances of winning reelection using a statistical hypothesis-testing procedure, we should first define the null and alternative hypotheses. The null hypothesis (H0) would be that the governor will receive at least 80% of the vote in the northern part of the state, which is the historical benchmark required for a Republican to be reelected in that area. The alternative hypothesis (H1) would be that the governor will receive less than 80% of the vote in the northern part of the state.
The polling organization will conduct a survey of 2,000 voters to estimate the proportion of the vote the governor could receive. Suppose the poll suggests that the governor will receive 78% of the vote. We would then use a z-test for proportions to determine if this result is statistically significantly different from the 80% benchmark, accounting for the sample size and variability of the polling data.
If the p-value obtained from the test is less than the chosen level of significance (typically 0.05), we would reject the null hypothesis and conclude there is statistical evidence that the governor may not receive the requisite 80% for reelection. If the p-value is higher, we do not have enough evidence to reject the null hypothesis, and it would suggest that the governor may have a favorable chance of reaching the 80% threshold. It's important to also consider factors such as incumbency advantage and voter distribution in the decision-making process.