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 2016 by a sample of residents at the Tidelands Medical Center.

77	81	86	84	82	85	87	84	84	84	85	78

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

2. Develop a 98% confidence interval for the population mean. (Use t Distribution Table.) (Round your answers to 2 decimal places.)

3. Is the company’s claim that the “typical customer” spends 80 per month reasonable?

• Yes

• No

Answer 1

a)
the point estimate of the population mean = 83.08

b)

sample mean, xbar = 83.08
sample standard deviation, s = 3.0588
sample size, n = 12
degrees of freedom, df = n - 1 = 11

Given CI level is 98%, hence α = 1 - 0.98 = 0.02
α/2 = 0.02/2 = 0.01, tc = t(α/2, df) = 2.718

ME = tc * s/sqrt(n)
ME = 2.72 * 3.0588/sqrt(12)
ME = 2.402

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (83.08 - 2.718 * 3.0588/sqrt(12) , 83.08 + 2.718 * 3.0588/sqrt(12))
CI = (80.68 , 85.48)

c)

yes, because confidence interval does not contain 80