Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-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) 0.0360

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-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) 0.0360 < p < 0.0745
B) 0.0251 < p < 0.0854
C) 0.0323 < p < 0.0782
D) 0.0280 < p < 0.0826

Quizplus · Accepted Answer

We first need to find the sample proportion:
p-hat = 21/380 = 0.0553

Next, we need to find the standard error using the formula:
SE = sqrt[p-hat(1-p-hat)/n]
SE = sqrt[0.0553(1-0.0553)/380] = 0.0196

Using a 95% confidence level, we know that the critical value for a two-tailed test is 1.96.

Finally, we can construct the confidence interval using the formula:
p-hat ± z*SE
0.0553 ± 1.96(0.0196)
0.0553 ± 0.038
The lower bound is 0.0553 - 0.038 = 0.0173
The upper bound is 0.0553 + 0.038 = 0.0933

Therefore, the 95% confidence interval is 0.0323 < p < 0.0782. Option C matches this interval.

Use the Given Degree of Confidence and Sample Data to Construct