Question

You recently sent out a survey to determine if the percentage of adults who use social media has changed from 54%, which was the percentage of adults who used social media five years ago. Of the 2862 people who responded to the survey, 1704 stated that they currently use social media. a) Use the data from this survey to construct a 97% confidence interval estimate of the proportion of adults who use social media. Record the result below in the form of ( # , # ) . Round your final answer to four decimal places.

Answer 1

Given that,

Point estimate = sample proportion = = x / n = 1704 / 2862 = 0.5954

Z_/2 = 2.17

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.17 * (((0.5954 * (1 - 0.5954)) / 2862)

= 0.0199

A 97% confidence interval for population proportion p is ,

- E < p < + E

0.5954 - 0.0199 < p < 0.5954 + 0.0199

(0.5755 , 0.6153)