Using the z-distribution, it is found that the 95% confidence interval for the proportion of all U.S. adults who play video games is (0.4681, 0.5119). It means that we are 95% sure that the true proportion of all U.S. adults who play video games is between 0.4681 and 0.5119.
<h3>What is a confidence interval of proportions?</h3>A confidence interval of proportions is given by:
In which:
is the sample proportion.
- z is the critical value.
- n is the sample size.
In this problem, we have that:
- 95% confidence level, hence
, z is the value of Z that has a p-value of
, so
.
- 49% out of 2001 U.S. adults play video games, hence
.
The lower bound of the interval is:
The upper bound of the interval is:
The 95% confidence interval for the proportion of all U.S. adults who play video games is (0.4681, 0.5119). It means that we are 95% sure that the true proportion of all U.S. adults who play video games is between 0.4681 and 0.5119.
To learn more about the z-distribution, you can take a look at brainly.com/question/25730047