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	86	84	86	79	82	87	81	84	78	74	86

Click here for the Excel Data File

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

2. Develop a 90% 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 hours per week reasonable?

• Yes

• No

Answer 1

Mean X̅ = Σ Xi / n
X̅ = 991 / 12 = 82.5833
Sample Standard deviation SX = √ ( (Xi - X̅ )2 / n - 1 )
SX = √ ( 170.9162 / 12 -1 ) = 3.9418

Part a)

X̅ = 82.58

Part b)

Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.1 /2, 12- 1 ) = 1.796
82.5833 ± t(0.1/2, 12 -1) * 3.9418/√(12)
Lower Limit = 82.5833 - t(0.1/2, 12 -1) 3.9418/√(12)
Lower Limit = 80.54
Upper Limit = 82.5833 + t(0.1/2, 12 -1) 3.9418/√(12)
Upper Limit = 84.63
90% Confidence interval is ( 80.54 , 84.63 )

Part c)

No, since the value 80 does not lies in the interval, hence it is not reasonable.