Statistics Worksheet

STAT2112.10 Quiz # 5 NAME:____________________GWID:G_____________Fall 2022
sba (Takehome – Due before or at 7:30pm on Wednesday)
Question 1. A machine is newly installed in a factory to fill bags of flour. The standard weight of
each bag of flour is 2000 g’s. The installing company operates the machine for one day in order
to test and five samples of the output from the machine are recorded every hour. The average
results for each of the five samples are as follows: 1996, 2090, 2010, 2008, 1835, 1820, 2180,
2118 grams. The specification limits are + 2% of the target value. The installers completed the
installation based on the above measurements. Assume the variance for the production line (2)
is 100g.
1a. What is the capability index of this process (Cp)? ______________ 0.5 pt
1b. Is the company capable of producing within the customer’s specification limits: ?______
and why______________________ 0.5pt
Question 2. A machine at a Cereal manufacturing company fills boxes with bran flakes cereal.
The target weight for the filled boxes is 24 ounces. The company would like to use appropriate
control charts to monitor the performance of the machine. To develop the charts, the company
decides to sample and weigh five boxes of cereal each day (at 8:00 and 11:00 a.m. and 2:00,
5:00, and 8:00 p.m.) for 20 consecutive days. The data are summarized in the printout below.
Here are some summary statistics that may help you in answering the below questions
X bar bar (mean of MEANWT) = 23.9971 and R Bar (mean of RANGEWT) =0.1815
a. Construct mean chart (with zones). 1 pts
b. Construct R chart (with zones). 1 pts
c. What do the charts suggest about the stability of the filling process (whether the process is in
or out of statistical control)? Justify your answer using short rule criteria. 1pt/chart.
1
Question 3. This is the example that I tried to do in class last night which had two mistakes on it.
I fixed the mistakes and the data (and my summary statistics) are provided below. The example
is about establishing a p-chart for complications developed after open heart surgery in a hospital.
Data is collected monthly. We want to know whether the complication rates have been in
control (or out-of-control) during this period. Here is the data you need:
Month
SUM/Total:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
–
Comp.
14
12
10
12
9
7
9
11
9
12
10
7
12
9
15
13
7
10
8
5
12
9
7
9
15
12
8
2
9
10
294
Procedure
105
97
11
100
95
111
68
47
83
108
115
94
107
99
105
110
97
105
71
48
95
110
103
95
105
100
116
110
105
120
2,835
3a. Using the average complication rate as the baseline, what is the minimum sample size is
required to this study? 0.5 pt
3b. Do you adequate sample sizes for this study? 0.5pt
3c. List the months during which the sample size was/were NOT adequate? 0.5pt
3d. Construct p-chart (with all the zones) based on average sample 1pts
2