The manager of a U.S. private hospital is conducting a study at the maternity unit to analyze the number of complaints at the nurse station made by families giving birth. For this purpose, he collected data from 20 weeks to create 20 samples (corresponding to each week) of 100 births each. He also gathered information on whether a birth gave rise to a complaint or not. The table below summarizes the data collected:
|
Week
|
Births
|
Complaints
|
|
Week
|
Births
|
Complaints
|
|
1
|
100
|
23
|
|
11
|
100
|
21
|
|
2
|
100
|
21
|
|
12
|
100
|
21
|
|
3
|
100
|
25
|
|
13
|
100
|
21
|
|
4
|
100
|
27
|
|
14
|
100
|
38
|
|
5
|
100
|
24
|
|
15
|
100
|
19
|
|
6
|
100
|
20
|
|
16
|
100
|
30
|
|
7
|
100
|
27
|
|
17
|
100
|
22
|
|
8
|
100
|
33
|
|
18
|
100
|
18
|
|
9
|
100
|
23
|
|
19
|
100
|
26
|
|
10
|
100
|
25
|
|
20
|
100
|
21
|
|
|
|
|
|
|
|
|
|
Total births samples: 2000
Total number of Complaints: 485
a) The hospital manager wants to use a P-chart to analyze the results. He started by plotting the fraction of births that gave rise to complaints, for each sample (see chart below). You are asked to complete this P-chart.
b) Does the P-chart provide evidence to support that the complaint process at the maternity unit is in-control? Explain your answer.
c) How would you use your results in part (b) to reduce the number of complaints?