Question

You recently sent out a survey to determine if the percentage of adults who use social media has changed from 62%, which was the percentage of adults who used social media five years ago. Of the 2371 people who responded to survey, 1650 stated that they currently use social media.

a) Use the data from this survey to construct a 93% 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.

• Yes, because the proportion of adults who used social media five years ago is inside of the confidence interval.
• Yes, because the proportion of adults who used social media five years ago is not inside the confidence interval.
• No, because the proportion of adults who used social media five years ago is inside the confidence interval.
• No, because the proportion of adults who used social media five years ago is not inside the confidence interval.

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

• The percentage increased.
• The percentage decreased.
• We cannot determine that the percentage has changed.

Answer 1

Answer:

a)

Given,

To determine the interval

p^ = x/n

= 1650/2371

p^ = 0.6959

Now at 93% confidence interval the critical value is z = 1.812

Interval = p^ +/- z*sqrt(p^(1 - p^)/n)

substitute the known values

= 0.6959 +/- 1.812*sqrt(0.6959(1 - 0.6959)/2371)

= 0.6959 +/- 0.01712

= (0.6959 - 0.01712 , 0.6959 + 0.01712)

Interval = (0.6788 , 0.7130)

b)

Here by observing we can say that option B is correct answer

i.e.,

Yes, because the the proportion of adults who used social media five years ago is not inside the

confidence interval.

c)

Here we can say that, if it has changed, the percentage decreased.

i.e.,

Option B is right answer.