A Rasmussen Reports survey of 1,000 US adults found that 42% believe raising the minimum wage will help the economy. Construct a 99% confidence interval for the true proportion of US adults who believe this.

Answer:(0.3798, 0.4602)Step-by-step explanation:Let p be the true proportion of US adults who believe raising the minimum wage will help the economy. A point estimate for p is [tex]\hat{p}=0.42[/tex] and a good aproximation (because we have a large sample) for the standard deviation of [tex]\hat{p}[/tex] is [tex]\sqrt{\hat{p}(1-\hat{p})/n}=\sqrt{0.42(0.58)/1000}=0.0156[/tex]. Therefore, a 99% confidence interval for p is given by [tex]\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}[/tex] where [tex]\alpha=0.01[/tex] and [tex]z_{\alpha/2}[/tex] is the [tex]\alpha/2[/tex]th quantile of the standard normal distribution, so we have, [tex]0.42\pm z_{0.005}0.0156[/tex], i.e., [tex]0.42\pm(-2.5758)(0.0156)[/tex] or equivalently (0.3798, 0.4602).