MSTL-002 Assignment Solution 2021
- AUTHOR: Narendra Kr. Sharma
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Content |
Pages |
Solution Booklet |
61 |
Question-1 |
Page 1-28 |
Question-2 |
Page 29-39 |
Question-3 |
Page 40-48 |
Question-4 |
Page 49-61 |
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MSTL-002 Assignment Sample Solution
MSTL-002 Assignment Question Paper
MSTL-002: Industrial Statistics Lab Download Question Paper
Note:
- All questions are compulsory.
- Solve the following questions in MS Excel 2007.
- Take the screenshots of the final output/spreadsheet.
- Paste all screenshots in the assignment booklet with all necessary hypotheses, interpretation, etc.
Q 1 The marketing manager of a transportation network company offering taxi services in a metro city wanted to study the waiting times of customers to get a taxi during the peak hours. A subgroup of 15 customers was selected (one at each ten minutes interval during the hour) and the time in minutes was measured from the point each customer booked the taxi to when he or she began the trip. The results of 40 days period were as under.
Sample No. |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
Obs. 1 |
8.7 |
6.6 |
6.7 |
5.6 |
6.9 |
8.2 |
7.3 |
5.7 |
Obs. 2 |
6.4 |
6.3 |
7.5 |
8.7 |
7.1 |
6.7 |
8.8 |
8.1 |
Obs. 3 |
8.8 |
7.3 |
9.5 |
7.1 |
10 |
7.2 |
7.1 |
5.2 |
Obs. 4 |
6.1 |
6.7 |
8.1 |
9.1 |
7.5 |
7.1 |
8.7 |
8.5 |
Obs. 5 |
8.6 |
8.5 |
9.3 |
6.9 |
9.8 |
7.1 |
8.9 |
7 |
Obs. 6 |
5.6 |
5.5 |
7.5 |
7.9 |
6.3 |
6.9 |
8 |
7.3 |
Obs. 7 |
8 |
7.9 |
8.7 |
6.3 |
9.2 |
6.5 |
8.3 |
4.4 |
Obs. 8 |
5.3 |
5.9 |
7.3 |
8.3 |
6.7 |
8 |
7.9 |
7.7 |
Obs. 9 |
5.8 |
5.8 |
7.7 |
8.1 |
6.5 |
7.7 |
8.2 |
7.5 |
Obs. 10 |
8.2 |
8.1 |
8.9 |
6.5 |
9.4 |
6.7 |
8.5 |
6.3 |
Obs. 11 |
5.5 |
6.1 |
7.5 |
8.5 |
6.9 |
6.5 |
8.1 |
7.9 |
Obs. 12 |
8.1 |
7.9 |
8.8 |
6.3 |
9.2 |
8.6 |
8.3 |
6.4 |
Obs. 13 |
6.5 |
6.4 |
8.7 |
9.1 |
7.3 |
6.8 |
8.9 |
8.4 |
Obs. 14 |
9.3 |
9.2 |
10.1 |
7.3 |
10.7 |
7.5 |
8.9 |
5 |
Obs. 15 |
6.1 |
6.8 |
8.4 |
9.6 |
7.7 |
7.3 |
9.2 |
8.9 |
Sample No. |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
16 |
Obs. 1 |
9.3 |
9 |
9 |
5.8 |
7.1 |
6 |
8.5 |
6.7 |
Obs. 2 |
8.5 |
8.2 |
7.2 |
7.9 |
7.7 |
7.3 |
10.7 |
8 |
Obs. 3 |
7.5 |
5.4 |
7.2 |
8.5 |
9.1 |
8 |
6.4 |
6.5 |
Obs. 4 |
8.7 |
8.6 |
7.7 |
8.3 |
8.5 |
7.7 |
11.1 |
8.4 |
Obs. 5 |
8.1 |
7.3 |
7 |
8.3 |
7.5 |
7.9 |
6.2 |
6.3 |
Obs. 6 |
7.8 |
7.4 |
6.5 |
7.1 |
8.6 |
6.5 |
9.9 |
7.2 |
Obs. 7 |
8.4 |
6.7 |
6.4 |
7.7 |
7.8 |
7.2 |
5.6 |
5.7 |
Obs. 8 |
7.3 |
7.8 |
6.9 |
7.5 |
8.1 |
6.9 |
10.3 |
7.6 |
Obs. 9 |
8.1 |
7.6 |
6.7 |
7.3 |
8.8 |
6.7 |
10.1 |
7.4 |
Obs. 10 |
8.6 |
4.8 |
6.6 |
8 |
8 |
7.5 |
5.8 |
5.9 |
Obs. 11 |
8.2 |
8 |
7.1 |
7.8 |
8.3 |
7.1 |
10.5 |
7.8 |
Obs. 12 |
7.5 |
4.6 |
6.4 |
7.8 |
8.8 |
7.3 |
5.6 |
5.8 |
Obs. 13 |
9.1 |
8.6 |
7.5 |
8.2 |
10 |
7.5 |
11.5 |
8.3 |
Obs. 14 |
9.7 |
7.7 |
7.4 |
9 |
9 |
8.4 |
6.5 |
6.6 |
Obs. 15 |
8.4 |
9.1 |
7.9 |
8.7 |
7.8 |
8 |
11.9 |
8.8 |
Sample No. |
17 |
18 |
19 |
20 |
21 |
22 |
23 |
24 |
Obs. 1 |
8.6 |
6.3 |
6.6 |
5.5 |
6.8 |
8.1 |
7.2 |
5.6 |
Obs. 2 |
5.6 |
6.9 |
8.5 |
8.6 |
7 |
6.6 |
8.7 |
8 |
Obs. 3 |
8.7 |
8.6 |
7.5 |
7 |
9.9 |
7.1 |
9 |
5.1 |
Obs. 4 |
6 |
5.2 |
8.6 |
9 |
7.4 |
7 |
7.9 |
8.4 |
Obs. 5 |
8.5 |
8.4 |
6.8 |
6.8 |
9.7 |
7 |
8.8 |
6.9 |
Obs. 6 |
6.6 |
5.4 |
7.6 |
7.8 |
6.2 |
8 |
7.9 |
7.2 |
Obs. 7 |
7.9 |
7.8 |
8.6 |
6.2 |
9.1 |
6.4 |
8.2 |
4.3 |
Obs. 8 |
5.2 |
5.8 |
7.8 |
8.2 |
6.6 |
6.2 |
7.1 |
7.6 |
Obs. 9 |
5 |
6.4 |
7.8 |
8 |
6.4 |
6 |
8.1 |
7.4 |
Obs. 10 |
8.1 |
8 |
8.8 |
6.4 |
9.3 |
6.6 |
8.4 |
4.5 |
Obs. 11 |
5.4 |
4.6 |
8 |
8.4 |
6.8 |
6.4 |
7.4 |
7.8 |
Obs. 12 |
8 |
7.8 |
8.7 |
6.2 |
9.1 |
6.4 |
8.2 |
6.3 |
Obs. 13 |
7.6 |
6.3 |
8.8 |
9 |
7.1 |
6.7 |
9.1 |
8.3 |
Obs. 14 |
9.2 |
9 |
10 |
7.1 |
10.5 |
7.3 |
9.5 |
8.3 |
Obs. 15 |
6 |
6.7 |
9 |
9.5 |
7.6 |
7.2 |
8.3 |
8.8 |
Sample No. |
25 |
26 |
27 |
28 |
29 |
30 |
31 |
32 |
Obs. 1 |
7.5 |
9.2 |
8.9 |
5.7 |
7 |
8.5 |
8.4 |
6.6 |
Obs. 2 |
8.1 |
8.1 |
7.1 |
7.8 |
9.3 |
7.2 |
10.6 |
7.9 |
Obs. 3 |
9.1 |
6.7 |
7.1 |
8.4 |
7.4 |
7.9 |
5.2 |
6.4 |
Obs. 4 |
7.9 |
8.5 |
7.6 |
8.2 |
8.1 |
7.6 |
11.7 |
8.3 |
Obs. 5 |
8.9 |
5.9 |
6.9 |
8.2 |
8.4 |
7.8 |
6.1 |
6.2 |
Obs. 6 |
7.3 |
7.3 |
6.4 |
7 |
8.5 |
6.4 |
9.8 |
7.1 |
Obs. 7 |
8.3 |
5.9 |
6.3 |
7.6 |
8.7 |
7.1 |
4.4 |
5.6 |
Obs. 8 |
7.2 |
7.7 |
6.8 |
7.4 |
7.3 |
6.8 |
10.9 |
7.5 |
Obs. 9 |
7.5 |
7.5 |
6.6 |
7.2 |
8.7 |
6.6 |
10 |
7.3 |
Obs. 10 |
8.5 |
6.2 |
6.5 |
7.9 |
8.9 |
7.4 |
4.6 |
5.8 |
Obs. 11 |
7.4 |
7.9 |
7 |
7.7 |
7.5 |
7 |
11.1 |
7.7 |
Obs. 12 |
8.3 |
5.3 |
6.3 |
7.7 |
7.9 |
7.2 |
5.5 |
5.7 |
Obs. 13 |
8.4 |
8.5 |
7.3 |
8.1 |
9.9 |
7.4 |
11.3 |
8.2 |
Obs. 14 |
9.6 |
6.9 |
7.2 |
8.8 |
8.9 |
8.3 |
5 |
6.5 |
Obs. 15 |
8.3 |
8.9 |
7.8 |
8.6 |
8.4 |
7.9 |
12.6 |
8.7 |
Sample No. |
33 |
34 |
35 |
36 |
37 |
38 |
39 |
40 |
Obs. 1 |
8.5 |
5.2 |
6.5 |
9.7 |
6.2 |
7.6 |
6.5 |
9.1 |
Obs. 2 |
8.1 |
5.7 |
7.4 |
7.8 |
8.5 |
8.3 |
7.8 |
11.5 |
Obs. 3 |
8.6 |
8.5 |
9.3 |
7.7 |
9.1 |
6.8 |
8.6 |
6.8 |
Obs. 4 |
5.9 |
6.6 |
7.1 |
8.2 |
8.9 |
9.1 |
8.3 |
11.9 |
Obs. 5 |
8.4 |
8.3 |
9.1 |
7.5 |
9 |
8 |
8.4 |
6.6 |
Obs. 6 |
7.3 |
4.9 |
7.3 |
6.9 |
7.6 |
6.2 |
7 |
10.6 |
Obs. 7 |
7.8 |
7.7 |
8.5 |
6.8 |
8.3 |
8.3 |
7.8 |
6 |
Obs. 8 |
5.1 |
5.8 |
6.4 |
7.4 |
8.1 |
8.7 |
7.4 |
11.1 |
Obs. 9 |
7.5 |
5.2 |
9.8 |
7.1 |
7.9 |
8.8 |
7.2 |
10.8 |
Obs. 10 |
8 |
7.9 |
8.7 |
7.1 |
8.5 |
8.6 |
8 |
6.2 |
Obs. 11 |
5.3 |
6.1 |
6.6 |
7.6 |
8.3 |
8.9 |
7.6 |
11.3 |
Obs. 12 |
7.9 |
7.7 |
8.6 |
6.9 |
8.3 |
9.3 |
7.8 |
6 |
Obs. 13 |
8.4 |
8 |
8.4 |
6.6 |
7.4 |
9.2 |
10.4 |
8.4 |
Obs. 14 |
9.1 |
8.9 |
9.9 |
7.3 |
7.2 |
9.7 |
10.2 |
8.1 |
Obs. 15 |
5.9 |
6.7 |
7.3 |
10.4 |
10.2 |
7.3 |
8.2 |
11.9 |
The manager of this company needs to construct the suitable control charts for variability as well as average to infer whether the waiting times of customers for getting a taxi is under control or not. If it is out-of-control, also construct the revised control charts.
Q 2 A publisher recorded the total number of pages in 25 published books and also the number of typing errors that have been made in preparing the final print of the books.
The results are given in the following table:
Day |
Number of pages |
Errors |
1 |
180 |
5 |
2 |
187 |
11 |
3 |
205 |
11 |
4 |
180 |
25 |
5 |
180 |
11 |
6 |
172 |
5 |
7 |
183 |
11 |
8 |
194 |
16 |
9 |
187 |
14 |
10 |
180 |
4 |
11 |
198 |
16 |
12 |
216 |
8 |
13 |
198 |
16 |
14 |
198 |
14 |
15 |
187 |
5 |
16 |
172 |
11 |
17 |
180 |
8 |
18 |
201 |
16 |
19 |
187 |
5 |
20 |
190 |
11 |
21 |
180 |
8 |
22 |
198 |
6 |
23 |
180 |
14 |
24 |
180 |
8 |
25 |
169 |
11 |
26 |
150 |
7 |
27 |
156 |
14 |
28 |
150 |
14 |
29 |
150 |
17 |
30 |
144 |
14 |
31 |
162 |
7 |
32 |
156 |
14 |
33 |
150 |
16 |
34 |
180 |
18 |
35 |
156 |
4 |
36 |
144 |
21 |
37 |
150 |
9 |
38 |
164 |
15 |
39 |
156 |
16 |
40 |
150 |
5 |
The publisher needs to set up a suitable control chart for the number of errors to check whether the number of errors in a state of control or not. Also computes the revised
control limits, if necessary.
Q 3 A researcher is interested to check the relationship between the salaries of workers involved in the production process of a company. To accomplish this, she/he has decided to develop a multiple regression model to predict their weekly salaries. For this purpose, he/she has selected a random sample of 50 workers involved in the production process. The information on their current monthly salaries in hundreds (Y), lengths of employment in months (X1), and job classifications (X2; 0 for technical job and 1 for clerical job) are summarised in the following table:
Employee |
Y |
X1 |
X2 |
1 |
495 |
74 |
1 |
2 |
406 |
51 |
0 |
3 |
567 |
130 |
1 |
4 |
523 |
25 |
1 |
5 |
575 |
178 |
1 |
6 |
437 |
42 |
0 |
7 |
664 |
242 |
1 |
8 |
491 |
57 |
1 |
9 |
472 |
72 |
0 |
10 |
407 |
129 |
1 |
11 |
378 |
17 |
1 |
12 |
725 |
318 |
1 |
13 |
600 |
296 |
0 |
14 |
440 |
39 |
0 |
15 |
662 |
280 |
1 |
16 |
523 |
116 |
1 |
17 |
428 |
19 |
1 |
18 |
535 |
94 |
1 |
19 |
533 |
193 |
0 |
20 |
528 |
49 |
1 |
21 |
446 |
26 |
0 |
22 |
528 |
40 |
1 |
23 |
498 |
51 |
1 |
24 |
478 |
48 |
1 |
25 |
507 |
32 |
0 |
26 |
478 |
24 |
1 |
27 |
645 |
234 |
1 |
28 |
577 |
281 |
0 |
29 |
554 |
335 |
1 |
30 |
654 |
336 |
1 |
31 |
566 |
77 |
1 |
32 |
433 |
90 |
0 |
33 |
466 |
89 |
1 |
34 |
365 |
30 |
0 |
35 |
677 |
225 |
0 |
36 |
473 |
36 |
1 |
37 |
644 |
305 |
1 |
38 |
685 |
316 |
1 |
39 |
356 |
11 |
0 |
40 |
444 |
23 |
1 |
41 |
478 |
94 |
0 |
42 |
408 |
81 |
0 |
43 |
456 |
58 |
0 |
44 |
409 |
22 |
0 |
45 |
691 |
359 |
0 |
46 |
463 |
69 |
0 |
47 |
436 |
93 |
0 |
48 |
413 |
16 |
1 |
49 |
734 |
412 |
0 |
50 |
463 |
69 |
0 |
- i) Prepare a scatter plot to get an idea about the relationship among the variables. ii) Fit a linear regression model and its related analysis at 1% level of significance. iii) Does the fitted regression model satisfy the linearity and normality assumptions?
- iv)Also, draw both fitted regression lines on the scatter plot.
Q 4 The marketing manager of a transportation network company offering taxi services in a metro city wishes to improve customer service and taxi scheduling based on the daily levels of customers in the past 10 weeks. The numbers of customers during that period are given below:
Week |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
Saturday |
Sunday |
1 |
334 |
499 |
262 |
232 |
435 |
351 |
223 |
2 |
170 |
249 |
203 |
268 |
329 |
168 |
293 |
3 |
110 |
179 |
240 |
114 |
266 |
99 |
90 |
4 |
155 |
234 |
81 |
253 |
314 |
93 |
278 |
5 |
95 |
164 |
225 |
99 |
264 |
107 |
283 |
6 |
270 |
183 |
308 |
125 |
194 |
255 |
129 |
7 |
223 |
132 |
239 |
268 |
143 |
323 |
332 |
8 |
212 |
369 |
390 |
369 |
218 |
495 |
320 |
9 |
479 |
540 |
414 |
590 |
390 |
460 |
663 |
10 |
549 |
739 |
734 |
684 |
642 |
866 |
832 |
- Determine the seasonal indices for the given data using a 7-day moving averages.
- Obtain the deseasonalised values.
- Fit the appropriate trend for the deseasonalised data using the least-squares method by matrix approach that best describes the data.
- Project the number of customers on Wednesday of the 52th
- Plot the original data, the de-seasonalised data, and the trend values.