No. of Printed Pages: 4 IMSTL-002lS21
POST GRADUATE DIPLOMA IN APPLIED STATISTICS (PGDAST)
Term-End Examination
June, 2016

MSTL-002/S2 INDUSTRIAL STATISTICS LAB SET-2
Time Hours Maximum Marks: 50
Note: Attempt any two questions.
Solve the questions in Microsoft Excel.
Use ofFormulae and Statistical Tables Booklet for PGDAST is allowed.
Mention necessary steps, hypothesis, interpretation, etc.
Symbols have their usual meanings.

1. A new production line is designed to dispense 12 ounces of a drink into each can as it passes along the line. Regardless of the care taken, there will be some variability in the amount of drink dispensed per can. The process will be considered out of control, if the mean amount of fill appears to differ considerably from the average fill obtained when the process is operating correctly or if the variability in fill appears to differ greatly from the variability obtained in a properly operating system. To check the process, the quality control inspector selects four cans (from the production line) each hour for a 24-hour period and measures the weight of each selected can. The results are given below:
Sample Number Weight per can
1 12.04 12.00 12.13 12.11
2 12.09 12.11 11.85 11.93
3 11.95 11.86 11.89 11.99
4 12.42 12.30 12.24 12.35
5 11.84 11.90 11.95 11.92
6 12.02 12.01 12.22 12.00
7 12.40 12.03 11.80 12.02
8 11.86 11.97 12.01 11.86
9 12.06 12.03 11.85 11.98
10 12.04 12.05 12.08 12.02
11 12.01 11.74 11.96 11.95
12 11.94 11.89 11.95 12.07
13 12.16 11.98 12.06 11.91
14 11.97 11.96 12.18 12.05
15 11.79 12.11 11.88 12.03
16 12.02 11.99 12.06 11.96
17 12.00 11.83 11.96 11.94
18 12.12 11.98 11.60 12.40
19 11.94 11.80 12.04 11.97
20 11.95 12.06 11.91 11.93
21 12.24 11.94 11.93 12.12
22 11.94 12.00 11.98 11.83
23 11.99 12.13 11.90 12.00
24 12.12 11.86 11.90 12.07

which control charts should be used to check whether the process is under statistical control or not?

Construct these charts and comment about the process on the basis of the charts.

Plot revised control charts, if necessary.

A quality control technician notes the number of defects (per 100 square metres) on paper, but the area of paper inspected for each sample varies. The results of20 inspections are shown in the following table:

Sample No. Area of Paper Inspected No. of Defects Sample No. Area of Paper Inspected No. of Defects
(in square metres) (in square metres)
1 300 7 11 200 5
2 200 8 12 250 9
3 250 5 13 100 6
4 150 5 14 250 8
5 250 10 15 300 6
6 100 4 16 250 5
7 200 5 17 150 9
8 150 8 18 200 7
9 150 8 19 150 6
10 250 6 20 300 10

Construct a suitable control chart for the number of defects per 100 square metres.

Comment whether the process is under statistical control or not.

Calculate the revised control limits, if necessary.

2. An agent of a real estate company would like to predict the selling price of a flat. The variables likely to be most closely related to selling price are the size of the flat, age of the flat, number of rooms in the flat and distance of the flat from the metro station. A random sample of 40 recently sold flats is taken and the selling price (in lakhs), the flat size (in square feet), age (in years), distance from the metro station (in kms) and the number of rooms in the flat are recorded as follows
Flat Selling Price (in lakhs) Flat Size (in square feet) Age (in years) Distance from Metro station (in kms) Number of Rooms
1 65.2 1316 10 1 2
2 68.0 1420 7 2 3
3 64.5 1550 5 4 2
4 66.0 1546 9 3 2
5 57.0 1354 8 2 2
6 75.0 1620 5 4 5
7 62.3 1300 15 2 3
8 64.5 1450 6 2 2
9 63.0 1380 4 4 2
10 64.8 1540 11 3 5
11 70.4 1600 5 2 5
12 64.7 1490 2 1 3
13 62.0 1370 5 3 3
14 77.3 1740 5 2 5
15 64.3 1460 7 3 4
16 59.5 1320 10 3 2
17 70.5 1400 4 1 5
18 64.3 1320 5 1 3
19 65.8 1550 10 2 3
20 68.8 1520 10 2 4
21 65.8 1438 15 4 3
22 66.2 1543 9 3 5
23 70.4 1520 10 1 5
24 60.0 1427 13 2 3
25 64.3 1460 2 4 4
26 63.4 1390 10 2 3
27 64.0 1410 5 5 4
28 75.5 1597 5 1 4
29 62.7 1374 4 2 3
30 63.4 1450 8 4 4
31 60.6 1490 15 3 5
32 75.4 1640 4 2 6
33 63.0 1395 5 4 4
34 56.1 1310 12 4 2
35 62.0 1520 15 3 5
36 68.2 1600 9 4 6
37 63.8 1530 12 2 5
38 68.4 1570 7 1 5
39 71.8 1410 4 2 4
40 64.5 1350 4 2 3

Build a regression model by selecting appropriate regressors in the model.

Estimate selling price of all the 40 flats using the above model.

3. The sales data of an automobile company during three financial years is given below:

Month Year
2013 2014 2015

April 524 1214 1043
May 1240 1917 1618
June 1406 1999 2680
July 1456 2383 1493
August 1349 2158 1936
September 2085 3477 3505
October 1323 1623 1731
November 1656 2172 1437
December 1935 2101 1546
January 1919 2561 2438
February 1875 1910 2455
March 3650 3796 3376

Compute the seasonal indices for 12 months using ratio-to-trend method.

Obtain deseasonalised values.

Plot the given data along with deseasonalised values.