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A poll conducted in 2013 found that 52% of U.S. adult Twitter users get at least some news on Twitter.40. The standard error for this estimate was 2.4%, and a normal distribution may be used to model the sample proportion. Construct a 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter, and interpret the confidence interval in context.

User ArgonQQ
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Answer: (0.458,0.582)

Explanation:

Given : Sample size :
n=815

The proportion of U.S. adult Twitter users get at least some news on Twitter. :
p=0.52

Standard error :
s.=0.024

Significance level :
\alpha: 1-0.99=0.01

Critical value :
z_(\alpha/2)=2.576

The confidence interval for population proportion is given by :-


p\pm\ z_(\alpha/2)\ s\\\\=0.52\pm(2.576)(0.024)\\\\\approx0.52\pm0.062=(0.52-0.062,0.52+0.062)=(0.458,0.582)

Hence, the 99% confidence interval for the fraction of U.S. adult Twitter users who get some news on Twitter, and interpret the confidence interval in context= (0.458,0.582)

User Yancyn
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