Question

In 2003, the Accreditation Council for Graduate Medical Education 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 week hours worked in 2017 by a sample of residents at the Tidelands Medical Center.

Resident	Hours Worked
1	84
2	86
3	84
4	86
5	79
6	82
7	87
8	81
9	84
10	78
11	74
12	86

Compute a 95% Confidence Interval in Excel with this data. Select the correct values set below for the 95% Confidence Interval (Lower,Upper).

Select one:

a. 81.44, 83.72

b. I have no idea how to do this.

c. 78.64, 86.52

d. 80.08, 85.09

Part B

Based on your 95% confidence interval calculation for the number of hours worked by graduate students, is the Tidelands Medical Center within the ACGME guideline? Why?

Select one:

a. No, because the mean of this sample is not within the computed Confidence Interval.

b. No, because the sample had a mean over the 80 hours per week set by the Accreditation Council for Graduate Medical Education.

c. Yes, because the mean of this sample is within +/- 3 standard deviation units.

d. Yes, because the mean hours worked of this sample is within the computed Confidence Interval.

Answer 1

Compute a 95% Confidence Interval in Excel with this data. Select the correct values set below for the 95% Confidence Interval (Lower,Upper).

Solution:

Here, we have to find the 95% confidence interval for the average number of hours worked in a week. The excel output for this confidence interval is given as below:

Confidence interval for Population mean

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	3.941811612
Sample Mean	82.58333333
Sample Size	12
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	1.137902998
Degrees of Freedom	11
t Value	2.2010
Interval Half Width	2.5045
Confidence Interval
Interval Lower Limit	80.08
Interval Upper Limit	85.09

Required Answer: d. 80.08, 85.09

Based on your 95% confidence interval calculation for the number of hours worked by graduate students, is the Tidelands Medical Center within the ACGME guideline? Why?

Answer:

a. No, because the mean of this sample is not within the computed Confidence Interval.

[See above confidence interval. Confidence interval is given as (80.08, 85.09) in which the population mean number of hours worked by graduate students is not included. The population man number of hours worked by graduate students is given as 80. ]