Question

The article “Doctors Cite Burnout in Mistakes” reported that doctors completing residency have financial struggles that could interfere with training. In a sample of 200 residents, 70 reported working a second job. Assume this is a random sample of all residents.

a. Construct a 95% confidence interval for the proportion of all residents who work a second job (round to two decimal places).

b. State the margin of error (round to two decimal places). _____

Answer 1

a) We need to construct the 95% confidence interval for the population proportion.

Let, X: number of residents reported working a second job.

x = 70

n = 200 ( sample size)

( proportion of all residents who work a second job )

The critical value for α=0.05 is Zc = Z1−α/2​= Z0.975 = 1.96. The corresponding confidence interval is computed as shown below:

b) The margin of error is given by