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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 (%)
5
15
20
25
30
35
40
Increase in sales (%)
5
10
18
25
35
50
60
65
1)Determine the value of ∑X, ∑X2, ∑Y, ∑Y2, ∑XY. Where X represent independent
variable and Y for dependent variable. [2]
2)Determine and interpret the coefficient of correlation between the two variables. [1]
3)Determine the value of regressions coefficients and write down the simple linear regression model. [1]
4)Test the validity of the model with the help of ANOVA. . [1]
5)Determine the tabulated values of “f” distribution at 0.1 level of significance. [1]
What does “R square” measure? What is its value and interpret it? [1]
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
Calculate the following [2]
Daily Production of Factory 1
Daily Production of Factory 1
Sample Size
Degree of freedom
Mean
Variance
Standard Deviation
1)Calculate the ratio of two variances and test the equality of the variances and comments.[1]
2)Calculate the value of pool standard deviation (Sp), degree of freedom in the light of part “b” and SED [1]
3)Write the null and alternative hypothesis for comparing the production of two factories. [1]
4)Calculate the critical values “ttab”, and tcal [1]
5)Write the conclusion for the null hypothesis of part “d”
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 (%)
5
15
20
25
30
35
40
Increase in sales (%)
5
10
18
25
35
50
60
65
1)Determine the value of ∑X, ∑X2, ∑Y, ∑Y2, ∑XY. Where X represent independent
variable and Y for dependent variable. [2]
2)Determine and interpret the coefficient of correlation between the two variables. [1]
3)Determine the value of regressions coefficients and write down the simple linear regression model. [1]
4)Test the validity of the model with the help of ANOVA. . [1]
5)Determine the tabulated values of “f” distribution at 0.1 level of significance. [1]
What does “R square” measure? What is its value and interpret it? [1]
The following is two years monthly sales data of 5 different 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
1) Write the null and alternate Hypothesis for the first two outputs.
2)Develop the ANOVA table for the calculation of “f distribution” value.
3) Find out the two critical values of “f distribution”.
4)Write the conclusion of the test.
For the random variable X with the probability function below, answer the following questions.
f(x)= { 3x^2 , 0<x<1
{ 0, otherwise
a. Find the cdf of X.
b. Find the probability that X is less than 0.5.
c. Find E(X).
For the random variable X defined by the probability function below, answer the following questions.
x 2 3 4 5 6 7
f(x) 0.25 0.15 0.10 0.15 0.10 0.25
a. Find the probability that X is even or at least 7.
b. Find and sketch the cdf.
c. Find the expected value and variance of X.
d. Find the expected value and variance of Y=2X+3.
The heights of 9-year-old children are normally distributed, with a mean of 123 cm and a standard deviation of 10 cm. Find the probability that the mean height of three randomly selected 9-year-old children is greater than 125 cm
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”
The following is two years monthly sales data of 5 different 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.
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?
#339914 on Dec 2023