Solve the problem.
-Of 357 randomly selected medical students, 30 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.
A)0.0462

Question

Solve the problem.
-Of 357 randomly selected medical students, 30 said that they planned to work in a rural community. Find a 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.
A)0.0462 < p < 0.122
B)0.0599 < p < 0.108
C)0.0553 < p < 0.113
D)0.0498 < p < 0.118

Quizplus · Accepted Answer

The 95% confidence interval for a proportion is calculated using the formula: $p \pm z\sqrt{\frac{p(1-p)}{n}}$, where $p$ 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, $p = \frac{30}{357}$, and $n = 357$. Plugging these values into the formula gives the interval 0.0553 < p < 0.113.

Solve the Problem. -Of 357 Randomly Selected Medical Students, 30 Said That They