1. A poll conducted in 2018 found that 54% of US adult Twitter users get at least some news on Twitter. The standard error for this estimate was 2.4%, and a normal distribution can be used to model the sample proportion. Construct a 99% confidence interval for the fraction of US adult Twitter users who get some news on Twitter, and interpret the confidence interval in context.

The 99% confidence interval for the fraction of US adult Twitter users who get some news on Twitter is (0.4872, 0.6018). It means that we are 99% sure that the true proportion of US adult Twitter users who get some news on Twitter is between 0.4872 and 0.6018.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of , and s is the standard error.

54% of US adult Twitter users get at least some news on Twitter.

This means that

The standard error for this estimate was 2.4%

This means that

99% confidence level

So , z is the value of Z that has a pvalue of , so

The lower bound is:

The upper bound is:

The 99% confidence interval for the fraction of US adult Twitter users who get some news on Twitter is (0.4872, 0.6018). It means that we are 99% sure that the true proportion of US adult Twitter users who get some news on Twitter is between 0.4872 and 0.6018.