Question

The following summary of a statistical study gives a sample statistic and a margin of error. Find the confidence interval and answer any additional questions. A poll is conducted the day before a state election for senator. There are only two candidates running for this office. The poll results show that 56 ​% of the voters favor the Republican​ candidate, with a margin of error of 4 percentage points. Should the Republican expect to​ win? Why or why​ not? Question content area bottom Part 1 The confidence interval is from    enter your response here​% to    enter your response here​%. ​(Simplify your answers. Use ascending​ order.) Part 2 The Republican ▼ is not is likely to win because ▼ ​50%.

Answer 1

Part 1: To find the confidence interval, you can use the margin of error (MOE) and the sample statistic. In this case, the sample statistic is 56%, and the margin of error is 4 percentage points.

To calculate the confidence interval, you would subtract the margin of error from the sample statistic for the lower bound and add the margin of error to the sample statistic for the upper bound.

Lower Bound: 56% - 4% = 52%

Upper Bound: 56% + 4% = 60%

So, the confidence interval is from 52% to 60%.

Part 2: The Republican candidate has 56% support in the poll, which is above the 50% mark. However, whether they can expect to win depends on several factors, including the margin of error, the actual voter turnout, and the distribution of votes on the election day.

While the poll shows the Republican candidate in the lead with 56%, there is a margin of error of 4 percentage points. This means that the true level of support for the Republican candidate could be as low as 52% (lower bound of the confidence interval) or as high as 60% (upper bound of the confidence interval).

In a two-candidate race, winning typically requires more than 50% of the vote. Since the lower bound of the confidence interval (52%) is above 50%, it suggests that the Republican candidate has a reasonable chance of winning based on this poll. However, it's important to consider the margin of error and other factors that can influence the election outcome.

The Republican candidate should be cautiously optimistic, but the final outcome will depend on the actual voter turnout and the distribution of votes on the election day.