91影视

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

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

$E=z_{\frac{伪}{2}}\sqrt{\frac{\hat{p}\hat{q}}{n}}$

$\hat{p}$ 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;

$z_{\frac{伪}{2}}$ is the two-tailed critical value of z.

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

$$\begin{gathered} \hat{p}=85\% \\ =\frac{85}{100} \\ =0.85 \end{gathered}$$

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

$$\begin{gathered} \hat{q}=1-\hat{p} \\ =1-0.85 \\ =0.15 \end{gathered}$$

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 $z_{\frac{伪}{2}}$ becomes equal to 1.96.

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

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

Thus, the margin of error is equal to 0.0221.