Question

bar graph
use the information below to answer the questions
the data in the accompanying bar graph are from a random sample of 890 adults
the graph shows four proposals to reduce gun violence in a country and the
percentage of surveyed adults who favored each of these proposals.
part a
find the margin of error for this survey round to the hundredth
part b
complete the statement about the percentage of adults in the countrys population
who favor a ban on high - capacity to reduce gun violence. (round to the hundredth)
there is a 95% confidence that between % and
% of all adults in the country favor a ban on high - capacity.

Explanation:

Part A

Step1: Recall the formula for margin of error

The formula for margin of error \(E\) for a proportion in a large - sample (when \(np\geq5\) and \(n(1 - p)\geq5\), which is likely for \(n = 890\)) with \(95\%\) confidence level is \(E=\frac{1}{\sqrt{n}}\).

Step2: Substitute \(n = 890\) into the formula

\(E=\frac{1}{\sqrt{890}}\approx\frac{1}{29.83}\approx0.0335\approx3.35\%\)

Part B

Step1: Use the formula for confidence interval

The confidence interval for a proportion is \(\hat{p}\pm E\). From the bar - graph, the proportion of adults who favored a ban on high - capacity (\(\hat{p}\)) is \(68\%=0.68\) (converted to decimal for calculation). The margin of error \(E = 0.0335\) (from Part A).

Step2: Calculate the lower and upper bounds

The lower bound is \(\hat{p}-E=0.68 - 0.0335=0.6465 = 64.65\%\)
The upper bound is \(\hat{p}+E=0.68+0.0335 = 0.7135=71.35\%\)

Answer:

Part A: \(3.35\%\)
Part B: There is a \(95\%\) confidence that between \(64.65\%\) and \(71.35\%\) of all adults in the country favor a ban on high - capacity.