Question

# The article “Doctors Cite Burnout in Mistakes” reported that doctors completing residency have financial struggles that...

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). _____

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

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