Of 380 randomly selected medical students, 21 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) 0.0251

Question

Of 380 randomly selected medical students, 21 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) 0.0251 < p < 0.0854
B) 0.0360 < p < 0.0745
C) 0.0280 < p < 0.0826
D) 0.0323 < p < 0.0782

Quizplus · Accepted Answer

The sample proportion is 21/380 = 0.0553. Using the formula for a confidence interval for a proportion, the 95% confidence interval is calculated as 0.0553 ± 1.96 * sqrt((0.0553*(1-0.0553))/380), which results in the interval 0.0323 < p < 0.0782.

Of 380 Randomly Selected Medical Students, 21 Said That They