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Q1. Following is the data related to the daily production of the two factories of same product located in two different states.
Factory
Daily Production
Factory 1
66
66
73
83
74
73
73
69
82
71
73
66
67
80
79
78
Factory 2
66
63
71
65
65
67
57
48
71
73
68
58
62
81
60
62
72
72
57
77
68
a. Calculate the following
Daily Production of Factory 1
Daily Production of Factory 1
Sample Size
Degree of freedom
Mean
Variance
Standard Deviation
b. Calculate the ratio of two variances and test the equality of the variances and comments.
c. Calculate the value of pool standard deviation (Sp), degree of freedom in the light of part “b” and SED
d. Write the null and alternative hypothesis for comparing the production of two factories.
e. Calculate the critical values “ttab”, and tcal
f Write the conclusion for the null hypothesis of part “d”
Breaking strength (in kg) of the front part of a new vehicle is normally distributed. In 10
trials the breaking strengths were found to be 578, 572, 570, 568, 572, 570, 570, 572, 596,
and 584. Can we say that the mean breaking strength is significantly less than 570 at 1%
level of significance? Further test the hypothesis at 5% level of significance.
Consider the following ten IQ scores. IQ test scores are scaled to have
a mean of 100 and a standard deviation of 15.
65 98 103 77 93 102 102 113 80 94
Test the hypothesis that the mean is 100.
If the probability is 0:75 that any person will believe a rumour, nd the probabilities
that (i) the fth person to hear it is the rst to believe it (ii) the eighth person to hear
the rumour will be the fth to believe it (iii) at least 4 persons do not believe the rumour
before the tenth person believes it.
There are 5 red balls and 2 green balls. What is the probability of picking a green ball if a ball is taken initially without replacing?
Let X be a random variable with the following probability distribution:
x : 3 6 9
P(X=x) : 1/6 1/2 1/3
Find E(X) and E(X^2)and using the laws of expectation, evaluate E . (2X+1)^2.
The following is two years monthly sales data of 5different outlets of a well-known textile brand. You are required to perform the analysis and answer the questions given below.
Brand
Sales in million Rs.
A
41
40
24
44
33
37
35
28
39
33
30
25
39
33
31
31
B
31
33
48
50
41
48
57
46
50
36
38
38
43
47
36
57
C
53
51
44
56
49
47
59
54
50
55
59
49
40
47
55
47
41
47
D
52
58
54
57
58
39
53
56
56
60
46
54
57
57
63
48
58
56
55
64
54
52
E
44
68
68
69
60
63
57
56
53
60
61
66
70
72
62
57
70
72
55
70
64
63
a. Write the null and alternate Hypothesis for the first two outputs.
b. Develop the ANOVA table for the calculation of “f distribution” value.
c. Find out the two critical values of “f distribution”.
Write the conclusion of the test.
A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results.
Increase in advertising expenditure (%)
0
5
15
20
25
30
35
40
Increase in sales (%)
5
10
18
25
35
50
60
65
a. Determine the value of ∑X, ∑X2, ∑Y, ∑Y2, ∑XY. Where X represent independent variable and Y for dependent variable.
b. Determine and interpret the coefficient of correlation between the two variables.
c. Determine the value of regressions coefficients and write down the simple linear regression model.
d. Test the validity of the model with the help of ANOVA.
e. Determine the tabulated values of “f” distribution at 0.1 level of significance.
f. What does “R square” measure? What is its value and interpret it?
Q1. Following is the data related to the daily production of the two factories of same product located in two different states.
Factory
Daily Production
Factory 1
66
66
73
83
74
73
73
69
82
71
73
66
67
80
79
78
Factory 2
66
63
71
65
65
67
57
48
71
73
68
58
62
81
60
62
72
72
57
77
68
a. Calculate the following
Daily Production of Factory 1
Daily Production of Factory 1
Sample Size
Degree of freedom
Mean
Variance
Standard Deviation
b. Calculate the ratio of two variances and test the equality of the variances and comments.
c. Calculate the value of pool standard deviation (Sp), degree of freedom in the light of part “b” and SED
d. Write the null and alternative hypothesis for comparing the production of two factories.
e. Calculate the critical values“ttab”, and tcal
f. Write the conclusion for the null hypothesis of part “d”
Q3. The following is two years monthly sales data of 5different outlets of a well-known textile brand. You are required to perform the analysis and answer the questions given below.
Brand
Sales in million Rs.
A
41
40
24
44
33
37
35
28
39
33
30
25
39
33
31
31
B
31
33
48
50
41
48
57
46
50
36
38
38
43
47
36
57
C
53
51
44
56
49
47
59
54
50
55
59
49
40
47
55
47
41
47
D
52
58
54
57
58
39
53
56
56
60
46
54
57
57
63
48
58
56
55
64
54
52
E
44
68
68
69
60
63
57
56
53
60
61
66
70
72
62
57
70
72
55
70
64
63
a. Write the null and alternate Hypothesis for the first two outputs.
b. Develop the ANOVA table for the calculation of “f distribution” value.
c. Find out the two critical values of “f distribution”.
d. Write the conclusion of the test.
