Question

As a hospital administrator of a large​ hospital, you are concerned with the absenteeism among​ nurses' aides. The issue has been raised by registered​ nurses, who feel they often have to perform work normally done by their aides. To get the​ facts, absenteeism data were gathered for the last three​ weeks, which is considered a representative period for future conditions. After taking random samples of 60 personnel files each​ day, the following data were​ produced:

                                                                                                                                       

Day	Aides Absent	Day	Aides Absent	Day	Aides Absent
1	6	6	6	11	3
2	5	7	1	12	8
3	1	8	7	13	12
4	3	9	2	14	4
5	7	10	8	15	4

Because your assessment of absenteeism is likely to come under careful​ scrutiny, you would like a type I error of only 1 percent. You want to be sure to identify any instances of unusual absences. If some are​ present, you will have to explore them on behalf of the registered nurses.

a. Design a​ p-chart.

The upper control limit is

______

and the lower control limit is

______

​(Enter your responses rounded to three decimal places. If your answer for the lower control limit is​ negative, enter this value as 0 .​)

Answer 1

a)

For p chart:

Sample size (n) = 60

Number of samples = Number of days = 15

p-bar = Total Aides absent/(Number of samples*n) = (6+5+1+3+7+6+1+7+2+8+3+8+12+4+4)/(15*60) = 0.0856

standard deviation (s) = sqrt(p-bar*(1-p-bar)/n) = sqrt(0.0856*(1-0.0856)/60) = 0.0361

For three sigma process, z = 3

Upper control limit = p-bar + z*s = 0.0856 + 3*0.0361 = 0.1939

Lower control limit = p-bar - z*s = 0.0856 - 3*0.0361 = - 0.0227. As it cannot be negative, it will be 0