Question 1
A market researcher of a trucking company intends to carry out a state wide survey concerning  truck repairs. He gathered data on the costs of all repairs performed by a truck owner during the  last year. The past experience of research suggests that the mean cost of repairs is $2,000. He collected data from 25 truck owners and found that the new mean cost of repairs was $2,250 with a standard deviation of $437. He wishes to find whether the population mean is different  to the sample mean.

a. State the null and the alternative hypothesis of the test.

b. At a 5% significance level, is there any evidence that the population mean is
different from $2,000?

c. Conduct the same test carried out in part (b) at a 1% significance level.

d. What are the p-values of the tests in parts (b) and (c)?

The management of a logistics company wishes to develop a method for allocating the delivery  costs to customers. Although one of the cost components clearly relates to the delivery time  within a particular route of delivery, another cost component relates to the time of unloading of boxes from trucks. A sample of 20 customers was selected from the existing routes and the delivery time and the numbers of boxes were estimated. The following are the results.

Customer Number of Boxes Delivery time (minutes)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
32
43
44
56
68
80
90
94
97
105
117
126
120
110
125
136
140
140
142
153
20.01
38.57
40.63
46.34
42.55
69.87
72.57
62.82
86.30
83.38
95.55
98.93
96.17
96.00
103.31
112.52
124.97
136.68
155.50
161.10
. Calculate the correlation coefficient and explain the relationship between the
number of boxes unloaded and the delivery time.

b. Present the data in a scatter diagram.

c. Use the least-square method to find the regression coefficients and state the
regression equation.

d. Interpret the meaning of coefficients of the regression equation in part (c).

e. Suppose, 160 boxes are to be delivered to a customer. Predict the delivery time.

f. At a 5% significance level, is there any evidence of a linear relationship between
delivery time and the number of boxes delivered?

A transport company plans to offer a new fast delivery parcel service. The new service has the  potential to capture a significant share of the deliveries resulting from internet shopping. The preliminary market and financial analysis showed the following price and cost elements of the service.

Service price = $40 per delivery
Administrative cost = $20,000
Advertising cost = $10,000

The labour cost, the cost of fuel, and the first year demand for this new service are not known and are considered to be probabilistic by nature. The direct labour costs are believed to have a discrete probability distribution as shown below.
The labour cost per delivery Probability
$20
$21
$22
$23
$24
0.1
0.2
0.3
0.3
0.1
The cost of fuel is described by a uniform distribution ranging from $8 to $10, and the first year demand is presumed to have a normal distribution with a mean of 5,500 deliveries with a standard deviation of 1,500. Using this information, the financial planner expects to carry out a simulation of financial risk analysis.

a) State the profit equation of the profit simulation model. bConduct a financial risk analysis for the new transport service using the following random numbers. (Clearly show the simulation results of labour costs, fuel costs and demand, mean, minimum and maximum profit and the probability of losses in your answer)
Random number for labour cost per delivery:

0.9007, 0.4176, 0.4850, 0.8846, 0.0949, 0.3009, 0.2280, 0.9496, 0.5530, 0.8742
Random number for fuel costs:
0.1001, 0.4561, 0.0824, 0.8462, 0.0434, 0.0899, 0.4603, 0.2937, 0.3142, 0.1614
Random number for demand:
0.4776, 0.5048, 0.8122, 0.1603, 0.3428, 0.9588, 0.8316, 0.6610, 0.5379, 0.1046
A terminal operator has planned to purchase an additional gantry crane as vessels with a high capacity are expected to call the port. Three alternative investments are possible under different demand conditions. The estimated profits of each investment decision under each economic condition are given in the following pay-off table.
Investment Decision
Events Buy a Panamax
gantry
Buy a Post
Panamax gantry
Buy a Super
Panamax gantry
Demand Declines $500 (-$2,000) (-$7,000)
No Change in the
Demand
$1,000 $2,000 (-$1,000)
Demand Expands $2,000 $5,000 $20,000
Based on the past trend in ship arrival data, the terminal operator assigns the following
probabilities to each demand condition.
P(Demand Declines) = 0.30
P(No Change in the Demand) = 0.50
P(Demand Expands) = 0.20

a. Determine the best investment decision according to the expected monetary value criterion. Explain the result.

b. Compute the expected opportunity loss for each possible investment decision.

c. What is meant by the expected value of perfect information (EVPI) and compute the expected value of perfect information (EVPI) for the above terminal investment
case.