Dr. Jordan operates a dental practice with 315 patients and she would like to estimate the proportion of her patients that have dental insurance from their employers. A random sample of 110 patients found that 40 had insurance coverage. The 95% confidence interval to estimate the proportion of patients with dental insurance is _____________.

Question

Quizplus · Accepted Answer

The 95% confidence interval for a proportion is calculated using the formula: $$CI = \hat{p} \pm z*\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$$ where $\hat{p}$ is the sample proportion, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), and $n$ is the sample size. Here, $\hat{p} = \frac{40}{110} = 0.3636$, and $n = 110$. Plugging these values into the formula gives a confidence interval of approximately (0.291, 0.437).

Dr Jordan Operates a Dental Practice with 315 Patients and She