Question

In 2003, the Accreditation Council for Graduate Medical Education (ACGME) implemented new rules limiting work hours for all residents. A key component of these rules is that residents should work no more than 80 hours per week. The following is the number of weekly hours worked in 2017 by a sample of residents at the Tidelands Medical Center.

84 84 84 90 79 81 84 88 86 78 74 84

1. What is the point estimate of the population mean? (Round your answer to 2 decimal places.)

2. Develop a 95% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)

3. Is the council's claim that the "typical resident" works 80 per month reasonable?

Answer 1

a)

Point estimate = 83.00

b)

sample mean, xbar = 83
sample standard deviation, s = 4.4107
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.2

ME = tc * s/sqrt(n)
ME = 2.2 * 4.4107/sqrt(12)
ME = 2.801

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (83 - 2.2 * 4.4107/sqrt(12) , 83 + 2.2 * 4.4107/sqrt(12))
CI = (80.20 , 85.80)

c)

yes, because confidence interval does not contain hypothesized value = 80