Question

Your assignment is to do a detailed statistical analysis of the data to be able to decide later what would be appropriate control charts to monitor these variables.

The manager provides you data that the office has collected on these two variables:

• Time it takes since the patient checks-in until the patient checks-out
• Number of patients in the waiting room

Present a report to the manager with the results of the statistical analysis of the data and your conclusions on the variables that will be used to monitor the process performance.

Time it takes since the patient checks-in until the patient checks-out
Observation	Time (minutes)
1	62.14
2	57.41
3	26.73
4	42.26
5	43.74
6	74.56
7	48.13
8	86.31
9	53.24
10	53.18
11	48.11
12	36.5
13	59.61
14	54.33
15	41.55
16	41.08
17	50.88
18	69.97
19	51.74
20	38.86
21	78.41
22	33.97
23	55.05
24	26.06
25	69.2
26	34.85
27	31.95
28	40.58
29	54.27
30	25.5
31	35.31
32	47.13
33	57.26
34	60.88
35	48.04
36	52.95
37	43.4
38	33.48
39	52.89
40	25.75
41	54.07
42	44.1
43	44.7
44	62.07
45	26.47
46	36.9
47	57.39
48	66.52
49	60.59
50	40.62
51	44.68
52	43.8
53	63.47
54	39.36
55	85.98
56	41.13
57	52.86
58	44.75
59	17.26
60	43.47
61	32.6
62	44.1
63	69.64
64	79
65	59.99
66	44.93
67	51.54
68	64.99
69	37.88
70	54.02
71	49.41
72	47.66
73	73.03
74	48.88
75	72.41
76	46.14
77	65.28
78	40.46
79	44.32
80	58.42
81	100.65
82	47.51
83	43.31
84	42.62
85	73.19
86	30.77
87	55.73
88	70.71
89	65.12
90	75.82
91	36.26
92	52.59
93	49.3
94	40.8
95	51.2
96	59.28
97	27.59
98	28.02
99	28.23
100	45.74

Answer 1

First of all, lets find out basic statics for the data
Mean          - 50.266 (Sum of the values/No. of values)
St Dev         - 15.268 (Average distance of each data point from the mean)
Variance      - 233.098 (Average squared distance of each data point from the mean)
N                - 100 (Sample size)
Minimum     - 17.260 (Min Value)
1st Quartile - 40.665 (25th percentile of the data)
Median        - 48.120 (Middle value)
3rd Quartile - 59.527 (75th percentile of the data)
Maximum    - 100.650 (Max value)

A-Squared   - 0.56

Formula

Notation

Term	Description
F(Yi)	, which is the cumulative distribution function of the standard normal distribution
Yi	ordered data

P-Value       - 0.141

If you know A² you can calculate the p-value. Let:

Depending on A'², you will calculate p with the following equations:

• If 13 > A'² > 0.600 then p = exp(1.2937 - 5.709 * A'² + 0.0186(A'²)²)
• If 0.600 > A'² > 0.340 then p = exp(0.9177 - 4.279 * A'² – 1.38(A'²)²)
• If 0.340 > A'² > 0.200 then p = 1 – exp(–8.318 + 42.796 * A'² – 59.938(A'²)²)
• If A'² <0.200 then p = 1 – exp(–13.436 + 101.14 * A'² – 223.73(A'²)²

Since the p-value is greater than 0.05 (level of significance or alpha), w can assume the data to be normally distributed

Since we are working on individual data points, we need to use Individual and moving range chart to understand the stabality of the data

Since the data is within 3 standard deviation limit, we can conclude the data is stable over time. except for one observation (81) we need to study, why is that so high, is there any special cause - if yes, we need to identify ways to prevent that in future.