Question

You recently sent out a survey to determine if the percentage of adults who use social media has changed from 56%, which was the percentage of adults who used social media five years ago. Of the 2519 people who responded to survey, 1718 stated that they currently use social media.

a) Use the data from this survey to construct a 98% 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.

b) Can you conclude that the percentage of adults who use social media has changed? Explain.

c)  If it has changed, has it increased or decreased?

Answer 1

a) Given that the out of n = 2519 people who responded to the survey, X = 1718 stated that they currently use social media.

So, the sample proportion would be:

Now the confidence interval is calculated as:

Where the Zc at 98% confidence level is computed using the excel formula for Z distribution which is =NORM.S.INV(0.99) thus the Zc is computed as 2.33.

= { 0.6604, 0.7036}

b) Now we can conclude that the percentage of adults who use social media has changed, because as we can see in the confidence interval limit that the range does not have the value of 0.56.

c) So, precisely we can state that it has increased because the lower limit is greater than that of the 0.56.