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

The 99% confidence interval for the population proportion is given by

$sample \ proportion \pm 2.575\times standard \ error$

Given that 52% = 0.52 is the standard proportion and the standard error is 2.4% = 0.024.

Therefore, the 99% confidence interval for the fraction of u.s. adult twitter users who get some news on twitter is given by

$0.52\pm2.575\times0.024=0.52\pm0.0618=(0.4582, \ 0.5818)$

Therefore, the 99% confidence interval for the fraction of u.s. adult twitter users who get some news on twitter is 45.82% and 58.18%.

The interpretation of the confidence interval is as follows: "We are 99% confident that the fraction of U.S. adult twiter users who get some news on twitter is between 45.82% and 58.18%.