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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 (%)
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. [2]
b. Determine and interpret the coefficient of correlation between the two variables. [1]
c. Determine the value of regressions coefficients and write down the simple linear regression model. [1]
d. Test the validity of the model with the help of ANOVA. . [1]
e. 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?
Geo-net, a cellular phone company, has collected the following frequency distribution for the length of calls outside its normal customer roaming area:
Length (min.) Frequency
0 65 26
5 6 10 75
10 6 15 139
15 6 20 105
20 6 25 37
25+ 18
400
The sample mean (x–) for this distribution is 14.3 minutes, and the sample standard deviation is
3.7 minutes. Determine whether these data are normally distributed 1a = .052.
A farmer is trying out a planting technique that he hopes will increase the yield on his pea plants. The average number of pods on one of his pea plants is 145 pods with a standard deviation of 100 pods. This year, after trying his newplanting technique, he takes a random sample of 144 his plants and finds the average number of pods to be 147. Do the data provide sufficient evidence, at α=0.05, to conclude that the new planting technique is effective in increasing yield?
Oklahoma Oil company is considering to make a bid for shale oil development contract to be awarded by Government. The company has decided to bid for $2.2 billion. The company has estimated that it has a 60% of winning the contract with this bid. If the firm wins the contract, it can choose one of three methods for getting the oil from the shale: It can develop a new method for oil extraction; Use an existing (inefficient) process, or subcontract the processing out to a number of smaller companies once the shale has been extracted. The results from these alternatives are given below:
Outcomes Probability Profit ($'billion)
1 . Develop New Method
Great success 0.30 12.00
Moderate success 0.60 6.00
Failure 0.10 -2.00
2 . Use Existing Process
Great success 0.50 6.00
Moderate success 0.30 4.00
Failure 0.20 -0.80
3 . Subcontract
Moderate success 1.00 5.00
The cost of preparing the contract proposal is $0.04 billion. If the company does not make a bid, it will invest into an alternative venture with a guaranteed profit of $0.6 billion.
Required:
(a) Construct a sequential decision tree for this decision situation. (7 marks)
(b) Determine whether the company should make a bid. (7 marks)
(c) Write a report to management at Oklahoma Oil company explaining
(i) Value of perfect information (2 marks)
(ii) Any three decision criteria suitable in an uncertain environment (9 marks)
(Total: 25 marks)
Mary is playing a game in which she rolls one die and spins a spinner. What is the probability she will get both the 3 and black she needs to win the game?
A contractor estimates the probabilities for the number of days required to complete a certain type of project as follows:
Time (days) 1 2 3 4 5
Probability 0.04 0.21 0.34 0.31 0.10
(4) If the contractor's project cost is made up of two parts: a fixed cost of $100 million plus $10 million for each day taken to complete the project, find the variance of total project costs. (3 Marks)
Question 2 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.
What does “R square” measure? What is its value and interpret it?
Question 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
a. Calculate the following
Daily Production of Factory 1
Sample Size
Degree of freedom
Mean
Variance
Standard Deviation
Daily Production of Factory 2
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
Write the conclusion for the null hypothesis of part “d”
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 [2]
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.[1]
c. Calculate the value of pool standard deviation (Sp), degree of freedom in the light of part “b” and SED [1]
d. Write the null and alternative hypothesis for comparing the production of two factories. [1]
e. Calculate the critical values “ttab”, and tcal [1]
f. Write the conclusion for the null hypothesis of part “d” [1]
A Computer Science class of BS-I contains 15 girls and 20 boys of which half the girls
and half the boys read Statistics in intermediate. Find the probability that a student chosen at
random is girl or has Statistics .
