Question

As a member of a management team, you are concerned with the absenteeism among​ assistants. The issue has been raised by your management team, who feel they often have to perform work normally done by their assistants. 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 65 personnel files each​ day, the following data were​ produced:

                                                                                                                                       

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

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 management team.

a. Design a​ p-chart.

The upper control limit

the lower control limit ​

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

b. Based on your​ p-chart and the data from the last 3​ weeks, what can you conclude about the absenteeism of​ Assistants?

Use the control limits from part​ (a) to determine if the process is out of control in the last 3 weeks. If any of the sample points fall outside of the control​ limits, then the process it out of statistical control.

Answer 1

Total Number of Absenteeism = 3+7+5+4+6+2+3+2+3+5+5+7+11+4+2 = 69

Total Sample Size np = 65*15 = 975

p-bar = Total Number of Absenteeism/np

p-bar = 69/975

p-bar = 0.07077

For Type 1 error of 1%, Z = 2.576

UCLp = p-bar + Z*(p-bar*(1-p-bar)/n)^(1/2)

UCLp = 0.07077 + 2.576*(0.07077*(1-0.07077)/65)^(1/2)

UCLp = 0.15270

UCLp = 0.153

LCLp = p-bar - Z*(p-bar*(1-p-bar)/n)^(1/2)

LCLp = 0.07077 - 2.576*(0.07077*(1-0.07077)/65)^(1/2)

LCLp = -0.01117

LCLp = 0.000

Below is the screenshot of the formula applied in excel -

Below is the screenshot of the p chart -

Since one sample is outside the control limit range, hence we can conclude that process is out of statistical control.