Question

checkpoint question: we now have all of the necessary values to calculate the confidence interval in our warm-up. which of the following expressions can be used to calculate this 99% confidence interval for p? 0.48±2.576 0.48±2.576(0.0156) 0.52±0.0156 0.52±2.576(0.0156) 0.48±0.0156 rewatch

Explanation:

Step1: Recall the formula for confidence interval for proportion

The formula for a confidence interval for a proportion \(p\) is \(\hat{p}\pm z_{\alpha/2}\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\), where \(\hat{p}\) is the sample proportion, \(z_{\alpha/2}\) is the critical value, and \(\sqrt{\frac{\hat{p}(1 - \hat{p})}{n}}\) is the standard error. Let's assume that \(\hat{p}=0.48\) (since \(0.48+0.52 = 1\) and we are dealing with a proportion, and the critical value \(z\) for a \(99\%\) confidence interval is \(z_{0.005}=2.576\). Let the standard error \(SE = 0.0156\)

Step2: Substitute into the formula

Substituting \(\hat{p}=0.48\), \(z = 2.576\) and \(SE=0.0156\) into the formula \(\hat{p}\pm z\times SE\), we get \(0.48\pm2.576(0.0156)\)

Answer:

\(0.48\pm2.576(0.0156)\)