Question

Critical Thinking: What does the survey tell us? Surveys have become an integral part of our lives. Because it is so important that every citizen has the ability to interpret survey results, surveys are the focus of this project. The Pew Research Center recently conducted a survey of 1007 U.S. adults and found that 85% of those surveyed know what Twitter is.

Analyzing the Data

Identify the margin of error for this survey

Short answer

The margin of error is equal to 0.0221.

Step-by-step solution

Given information

A survey consisted of 1007 U.S. adults. 85% of those who were surveyed know what Twitter is.

Margin of error

The margin of error (E) has the following formula:

\(E = {z_{\frac{\alpha }{2}}}\sqrt {\frac{{\hat p\hat q}}{n}} \)

Where

\(\hat p\)is the sample proportion of adults who know what Twitter is;

\(\hat q\)is the sample proportion of adults who do not know what Twitter is;

n is the sample;

\({z_{\frac{\alpha }{2}}}\)is the two-tailed critical value of z.

Calculation

The proportion of adults, who know what Twitter is, is shown below:

\(\begin{array}{c}\hat p = 85\% \\ = \frac{{85}}{{100}}\\ = 0.85\end{array}\)

The proportion of adults, who do not know what Twitter is, is shown below:

\(\begin{array}{c}\hat q = 1 - \hat p\\ = 1 - 0.85\\ = 0.15\end{array}\)

The sample size (n) is equal to 1007.

For the confidence level of 95%, the level of significance is equal to 0.05.

Using the standard normal table, the value of\({z_{\frac{\alpha }{2}}}\)becomes equal to 1.96.

Substituting these values, the margin of error becomes as follows:

\(\begin{array}{c}E = {z_{\frac{\alpha }{2}}}\sqrt {\frac{{\hat p\hat q}}{n}} \\ = \left( {1.96} \right)\sqrt {\frac{{0.85\left( {0.15} \right)}}{{1007}}} \\ = 0.0221\end{array}\)

Thus, the margin of error is equal to 0.0221.