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 60​% of the voters favor the Republican​ candidate, with a margin of error of 3 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 is not likely to win because ▼ both endpoints of the confidence interval are less than both endpoints of the confidence interval are greater than one endpoint of the confidence interval is less than one endpoint of the confidence interval is greater than ​50%.

Answer 1

The confidence interval is from 57% to 63%. Since both endpoints of the confidence interval are above 50%, the poll suggests the Republican candidate is likely to win, assuming the poll reflects the actual voter population accurately.

Step-by-step explanation:

The confidence interval can be calculated by taking the sample statistic (point estimate) and adding and subtracting the margin of error. In this case, the poll shows that 60% of voters favor the Republican candidate with a margin of error of 3 percentage points. Therefore, the confidence interval is from 57% to 63% (60% - 3%, 60% + 3%).

The question of whether the Republican candidate should expect to win is not straightforward. While the poll suggests a lean towards the Republican candidate, actual election results can be affected by many variables not accounted for in the margin of error.

However, because both endpoints of the confidence interval are greater than 50%, the poll suggests that the Republican candidate is likely to win the election if it accurately reflects the voting population's choice, understanding that the actual vote percentage could still fall outside this interval due to factors like actual voter turnout or other variables not included in the poll's model.