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

Explain why it would or would not be okay for a newspaper to make this statement: “Based on results from a recent survey, more than 3 out of 4 adults know what Twitter is.”

Short answer

It would be correct for a newspaper to report that according to the survey results, more than 3 out of 4 adults know what Twitter is.

Step-by-step solution

Given information

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

Analysis of the statement

It is stated that according to the results of the survey, more than 3 out of 4 adults know what Twitter is.

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

\(\begin{array}{c}\frac{3}{4} = 0.75\\ = 75\% \end{array}\)

Referring to Exercise 7-1FDD, the 95% confidence interval estimate for the percentage of adults, who know what Twitter is, is equal to (82.8%, 87.2%).

This suggests that there is 95% confidence that the percentage of adults who know Twitter will lie between 82.8% and 87.2%.

The value of 75% is undoubtedly greater than the lower limit of the confidence interval.

Thus, the statement that more than 3 out of 4 adults (75% adults) know what Twitter is is correct.