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SATHYABAMA UNIVERSITY
(Established under section 3 of UGC Act,1956)
Course & Branch :M.B.A - MBAF/W-MBA
Title of the Paper :Statistics for Management
Sub. Code :741207
Date :02/06/2011
Max. Marks :80
Time : 3 Hours
Session :AN
______________________________________________________________________________________________________________________
PART - A
(8 x 5 = 40)
Answer any EIGHT Questions
1. Calculate the Karl Pearson’s co-efficient of correlation for the
following heights(in inches) of fathers (X) and their sons(Y):
X
65
66
67
67
68
69
70
72
Y
67
38
65
68
72
72
69
71
2.
Fit a straight line to the following data:
X
1
2
3
4
Y
2.4
3
3.6
4
6
5
8
6
3.
An article manufactured by a company consists of two parts A
and B. In the process of manufacture of Part A, 9 out of 100 are
likely to be defective. Similarly, 5 out of 100 are likely to be
defective in the manufacture of part B. Calculate the probability
that the assembled article will not be defective (assuming that the
events of finding the part a non-defective and that of B are
independent)
4.
A father and his son appear in an interview for two vacancies in
1
the same post. The probability of father’s selection is 7 and that
1
of son’s selection is 5 . What is the probability that
(a) both of them will be selected (b) none of them will be
selected?
5.
A manufacturer of cotterpins knows that 5% of his product is
defective. IF he sells cotterpins in boxes of 100 and guarantees
that not more than 10 pins will be defective, what is the
approximate probability that a box will fail to meet the
guaranteed quality?
6.
The mean weekly sales of soap bars in departmental stores was
146.3 bars per store. After an advertising campaign the mean
weekly sales in 22 stores for a typical week increased to 153.7
and showed a standard deviation of 17.2. Was the advertising
campaign successful?
7.
Test the significance of the difference between the means of the
samples, drawn from two normal populations with the same
standard deviation using the following data:
Size
Mean
Standard deviation
Samples 1
100
61
4
Sample 2
200
63
6
8.
9.
The mean height and the standard deviation height of 8 randomly
chosen soldiers are 166.9 and 8.29 cm respectively. The
corresponding values of 6 randomly chosen sailors are 170.3 and
8.5 cm respectively. Based on these data, can we conclude that
soldiers are, in general, shorter than sailors?
Two researchers adopted different sampling techniques while
investigating the same group of students to find the number of
students falling into different intelligence level. The results are as
follows.
Researchers Below average Average Above average Genius Total
X
86
60
44
10
200
Y
40
33
25
2
100
Total
126
93
69
12
300
Would you say that the sampling techniques adopted by the two
researchers are significantly different. (Given 5% value of 2 for
2 degrees and 3 degrees of freedom are 5.991 and 7.82
respectively).
10. Explain one sample run test with an example.
11. The simple correlation coefficients between temperature (X),
corn yield (Y) and rainfall (Z) are r12 = 0.59, r13 = 0.46 and r23 =
0.77. Calculate the partial correlation coefficients r12.3 and r23.1.
12. If r12 = 0.8, r13 = -0.4 and r23 = -0.56. calculate the value of R1(23).
PART – B
(4 x 10 = 40)
Answer Any FOUR Questions
13. Cost accountants often estimate overhead based on the level of
production. At the standard knitting company, they have
collected information on overhead expenses and units produced
at different plants and want to estimate a regression equation to
predict future overhead.
Overhead 191 170 272 155 280 173 234 116 153 178
Units
40 42 53 35 56 39 48 30 37 40
(a) Develop the regression equation for the cost accountants.
(b) Predict overhead when 50 units are produced.
14. (a) In a certain factory turning out razor blades, there is a small
chance of 0.002 for any blade to be defective. The blades are
supplied in packets of 10. Use Poisson distribution to calculate
the approximate number of packets containing no defective, one
defective and two defective blades respectively in a consignment
of 2.00.000 packets.
(b) In a normal distribution , 31% of the items are under 45 and
8% are over 64. find the mean and standard deviation of the
distribution.
15. In a large consignment of electric bulbs 10% are defective. A
random sample of 20 is taken for inspection. Find the probability
that
(a) all are good bulbs
(b) at most there are 3 defective bulbs
(c)exactly there are 3 defective bulbs.
16. Steel wire was made by 4 manufacturers A, B, C and D. In order
to compare their products, 10 samples were randomly drawn
from a batch of wires made by each manufacturer and the
strength of each piece of wire was measured. The (coded) values
are given below:
A
55
50
80
60
70
75
40
45
80
70
B
70
80
85
105 65
100 90
95
100 70
C
70
60
65
75
90
40
95
70
65
75
D
90
115 80
70
95
100 105 90
100 60
Carry out an analysis of variance and give your conclusions.
17. Melisa’s Boutiques has three mall locations. Melisa keeps a daily
record for each location of the number of customers who actually
make a purchase. A sample of those data follows. Using the
Kruskal-Wallis’s test, can you say at the 0.05 level of
significance that her stores have the same number of customers
who buy?
Eastowne Mall
99 64 101 85 79 88 97 95 90 100
Craborchard Mall 83 102 125 61 91 96 94 89 93 75
Fairforest Mall
89 98 56 105 87 90 87 101 76 89
18. In a trivariate distribution, X 1 = 28.02, X 2 = 4.91, X 3 = 594,
S1 = 4.4, S2 = 1.1, S3 = 80, r12 = 0.80, r23 = -0.56, r31 = -0.40.
(a) Find the correlation coefficients r23.1 and R1.23.
(b) Also estimate the value of X1 when X2 = 6.0 and X3 = 650.