Discussion:
Q: A portion of the data file for the hospital that collected the data on hand washing is shown below:
Observation Unit Time 1 Time 2
1 CCU 3 16
2 CCU 2 7
3 CCU 0 5
4 CCU 5 8
5 CCU 2 15
6 CCU 0 15
7 CCU 2 20
8 CCU 3 16
9 CCU 0 18
10 IMCU 1 16
11 IMCU 2 8
You can see that information was also collected on the unit of the employee and a second time, labeled Time 2, was also recorded. Assume that the hand-washing times are normally distributed and are recorded in seconds.
a). Find the sample means and sample standard deviations for the first hand-washing time, Time 1, for each unit.
b). Test to see if any of the units had an average hand-washing time, Time 1, less than 5 seconds.
c). The second hand-washing time, Time 2 was recorded after the employees received some training on the effects of not washing their hands long enough. Find the sample means and sample standard deviations for the second hand-washing time, Time 2, for each unit.
d). Test to see if any of the units had an average hand-washing time after training, Time 2, of less than 5 seconds.
e). Display all the initial hand-washing times, Time 1 in a histogram. Is the assumption of normality reasonable?
f). Display all the second hand-washing times, Time 2, in a histogram. Is the assumption of normality reasonable?
g). Test the hypothesis that the variance of the initial hand-washing time is 14 seconds.
h). Test the hypothesis that the variance of the hand-washing times after training is greater than 14 seconds.
i). Find the sample proportion of employees who increased their hand-washing time after training. Test the hypothesis that the proportion of employees who increased their time after training is greater than 0.80.
j). Based on your analysis, write a short report to the manager of the hospital.