Question

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.

Answer 1

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)