Answer:
The 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter is between 49.34% and 60.66%, which means that we are 99% sure that the true percentage of US adult Twitter users who get some news is in this interval.
Step-by-step explanation:
Confidence interval:
A confidence interval has the following format:
[tex]M \pm zs[/tex]
In which M is the sample mean, z is related to the confidence level and s is the standard error.
55% of U.S. adult Twitter users get at least some news on Twitter (Pew, 2013). The standard error for this estimate was 2.2%.
This means that [tex]M = 55, s = 2.2[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
Lower bound of the interval:
[tex]M - zs = 55 - 2.575*2.2 = 49.34[/tex]
Upper bound:
[tex]M + zs = 55 + 2.575*2.2 = 60.66[/tex]
The 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter is between 49.34% and 60.66%, which means that we are 99% sure that the true percentage of US adult Twitter users who get some news is in this interval.
