Question

the data in the accompanying bar graph are from a random sample of 831 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. complete parts (a) and (b) below.
a. find the margin of error for this survey.
the margin of error is ±□%.
(do not round until the final answer. then round to the nearest tenth as needed.)
b. write a statement about the percentage of adults in the countrys population who favor required gun registration to reduce gun violence.
there is 95% confidence that between □% and □% of all adults in the country favor required gun registration.
(use ascending order. round to the nearest tenth as needed.)

Explanation:

Step1: Calculate the margin of error

The formula for the margin of error \(E\) for a proportion in a simple random sample is \(E = 1.96\sqrt{\frac{p(1 - p)}{n}}\). When \(p\) is unknown (which is often the case in a general margin - of - error calculation for a survey), we use \(p=0.5\) (this gives the maximum value of the margin of error). Here \(n = 831\).

First, calculate \(\sqrt{\frac{p(1 - p)}{n}}\):

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Then, calculate \(E\):

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Step2: Calculate the confidence interval for the proportion of adults who favor required gun registration

The sample proportion \(p_s=0.62\) (from the bar graph for required gun registration). The confidence interval is given by \(\hat{p}-E

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Answer:

a. The margin of error is \(\pm3.4\%\)
b. There is \(95\%\) confidence that between \(58.6\%\) and \(65.4\%\) of all adults in the country favor required gun registration.