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

a. What is the point estimate of the population mean for the number of weekly hours worked at the Tidelands Medical Center?

b. Develop a 90% confidence interval for the population mean.

c. Is the Tidelands Medical Center within the ACGME guideline? Why?

Answer 1

A)Point estimate of the population is the sample mean = sum(x)/n = 82.58

B)Confidence interval for population mean is

μ = M ± t(s_M)

where:

M = sample mean
t = t statistic determined by confidence level
s_M = standard error = √(s²/n)

M = 82.58
t = 1.8
s_M = √(3.94²/12) = 1.14

μ = M ± t(s_M)
μ = 82.58 ± 1.8*1.14
μ = 82.58 ± 2.0426 =(80.5374, 84.6226)

C)Null Hypothesis,H₀: The population mean is significantly not different from 80

Alternative Hypothesis,H_a: The population mean is less than 80

Test statistic is t = x(bar) - mu / s/√n

Then the value of t is 2.27

p value is .978

Since p value is greater than .1 , we accept the null hypothesis and conclude that the Tidelands Medical Center is not within the ACGME guideline