1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
ME SEMESTER-1 EXAMINATION WINTER 2018
Subject Code: 3712507 Date: 04/01/2019
Subject Name: Design of Experiment Statistical Techniques
Time: 02:30 PM To 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full mark
Q.1

Find Q1, Q3, D7 and P85 for the following frequency distribution.
Weight in lbs
115
120
130
140
145
No. of men
8
20
35
24
12
07

Following data represents average and range of liner density of the yarn obtained from eight different samples each of size five, selected during a spinning process.
Sample no.
1
2
3
4
5
6
7
8
Avg. linear density
19.6
20.1
20.5
19.4
22.3
21.7
20.3
19.9
Range
1.2
2.1
1.6
1.8
2.0
1.7
2.0
1.8
Draw the mean and range charts for the above data and comment on them. (Table value: A2 0.577, D3= D4=2.115)
07
Q.2

If the value of correlation coefficient between the two variable X and Y is 0.83, find the equation of regression of X on Y and Y on X using following data.
Variables
X
Y
Mean
112
65
Standard deviation
2.5
3.2
07

Explain Poisson probability distribution with their properties.
07
OR

Explain Binomial probability distribution with their properties.
07
Q.3

Following results are obtained from the 10 observations of the variables X1 X2 (strength) and X3 (%elongation)
X1
X2
X3
Mean
30.12
12.56
5.25
SD
2.12
1.50
0.80
Also, r12 -0.65, r13=-0.58 and r23= 0.62, using the above data find the multiple correlation coefficient of X3 with X1 and X2 and comment on the results
07

Following are the marks obtained by eight different students in the subject of mathematics and the subject of statistics.
Student No.
1
2
3
4
5
6
7
8
Marks in Mathematics
48
85
70
72
70
68
65
80
Marks in statistics
42
92
65
80
67
62
60
72
Calculate rank correlation coefficient using the above data and comment on it
07
OR
2
Q.3

Two ring frames are expected to spin the yarn of the same strength. The samples of 35 and 40 ring bobbins selected from these ring frames have shown following results.

R/F-II
Sample size
35
40
Mean strength
60 units
56 units
Std. deviation of strength
1.25 units
1.50 units
From the sample results, is there any evidence that the yarn of first ring frame is having strength more than the yarn of ring frame Use los. (Using Z test)
Z 0.01=2.33]
07

Following is the distribution of 200 samples of five garments each, according to the number of effective garments.
No. of defective garments
0
1
2
3
4
5
Total
No. of samples
50
80
40
15
10
5
200
Fit the binomial probability distribution to the above data and test the goodness of fit assuming, Probability of the defective garments "p" is unknown. 20% of the garments are defective. (d.f. at level X2 2,0.05 5.991 X2 3,0.05 7.815)
07
Q.4

Explain Normal distribution with their properties.
07

Compute Karl Pearson's coefficient of correlation form the following data of piece of garment (in Rs.) and Number of garments sold and comment on it.
Price of garment
100
105
110
115
120
125
130
Number of garment sold
85
80
70
75
65
60
60
07
OR
Q.4

Calculate the mean deviation about mean for the following data and comment on it.
Class
10-11
11-12
12-13
13-14
14-15
f
5
10
25
10
5
Calculate quartile deviation for the above data and comment on it.
07

Following are the results of sales of two types of knitted garments:
Type A
10
12
11
14
10
11
15
12
14
13
Type B
12
10
17
13
12
10
10
18
14
15
Find CV% and decide sale of which type of garment is more consistent.
07
Q.5

A 22 factorial experiment was conducted to study the effect of the speed of ring frame and thee traveler weight on the hairiness index of the yarn. The experiment was carried out by the spinning the yarn of three different count on the same The results of hairiness indices obtained from the samples are as follows:

R/F-II
R/F-III
7.8
10.0
6.5
6.2
8.5
9.5
10.2
7.5
7.0
8.2
6.8
8.2
Carry out the analysis of the above data and write the conclusion.
Table value for 6 degree of freedom at level 5.99
Table value for 6 degree of freedom at level 5.14
14
OR
3
Q.5

An experiment was conducted to study the effect of the speed of the ring frame on the count of the yarn. The yarn was spun with four different speeds on three different ring frame and the results yarn are as follows.
Analyze the above data using a two-way ANOVA and write conclusions.
table value for 24 degree of freedom at level 3.40]
table value for 24 degree of freedom at level 3.01]
table value for 24 degree of freedom at level 2.51]
Loom
Operator
15000
16000
17000
18000
I
85,80,82
88,85,86
85,82,84
80,82,84
II
79,82,80
85,80,78
80,86,83
85,88,86
III
80,81,80
82,85,84
88,85,86
84,85,86
14