A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameterof interest and answer the question.
-Ten years ago, according to government records, 17% of the population of Elmwood had no health insurance. This year a poll revealed that 20.6% were without insurance. The margin of error was 2.8 percentage points. Find a confidence interval for the true percentage without insurance this Year. Can we conclude that the percentage without insurance has increased from ten years ago?
A) $15 \%$ to $20.6 \%$; no
B) $20.6 \%$ to $23.4 \%$; yes
C) $19.2 \%$ to $22 \%$; yes
D) $17.8 \%$ to $23.4 \%$; yes

Question

A sample statistic and margin of error are given. Find the confidence interval likely to contain the population parameterof interest and answer the question.
-Ten years ago, according to government records, 17% of the population of Elmwood had no health insurance. This year a poll revealed that 20.6% were without insurance. The margin of error was 2.8 percentage points. Find a confidence interval for the true percentage without insurance this Year. Can we conclude that the percentage without insurance has increased from ten years ago? 
A) $15 \%$ to $20.6 \%$; no
B) $20.6 \%$ to $23.4 \%$; yes
C) $19.2 \%$ to $22 \%$; yes
D) $17.8 \%$ to $23.4 \%$; yes

Quizplus · Accepted Answer

The confidence interval is calculated by adding and subtracting the margin of error from the sample statistic. Therefore, $20.6\% \pm 2.8\% = [17.8\%, 23.4\%]$. Since the interval does not include the previous percentage of 17%, we can conclude that the percentage without insurance has likely increased.

A Sample Statistic and Margin of Error Are Given 15%15 \%15%

A Sample Statistic and Margin of Error Are Given $15 \%$