A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameterof interest and answer the question.
-Following the Republican National Convention, a poll of voters in a Central Illinois community showed that 58.1% would choose the Republican ticket to win over the Democrat ticket no matter
Whom the Democrats chose for vice-president. The margin of error was 4.2 percentage points.
Should the Democrats expect to lose Central Illinois?
A)53.9% to 62.3%; yes
B)49.7% to 58.1%; no
C)58.1% to 62.3%; yes
D)56% to 60.2%; yes

Question

Quizplus · Accepted Answer

The confidence interval is calculated by subtracting and adding the margin of error to the sample statistic. 58.1% - 4.2% = 53.9% and 58.1% + 4.2% = 62.3%. Since the interval does not include 50%, it suggests the Republicans would win, so the Democrats should expect to lose.

A Sample Statistic and Margin of Error Are Given