Perform rank correlation analysis on the following data set:
| x | y |
|---|---|
| -3 | -0 |
| -2.65 | -1.3 |
| -2.15 | -1.5 |
| -1.85 | -1.5 |
| -1.55 | -1.7 |
| -1.2 | -1.3 |
| -0.8 | -0.5 |
| -0.4 | -0.9 |
| -0.1 | 0 |
| 0.4 | 0.9 |
| 0.75 | -0.3 |
| 1.1 | 1.4 |
| 1.6 | 1.4 |
| 1.95 | 0.3 |
| 2.4 | 1.3 |
| 2.7 | -0.6 |
| 3 | -0.9 |
| 3.55 | 0.4 |
| 4 | 0 |
| 4.5 | -0.9 |
What is the rank correlation coefficient? (Round to three decimal places.)
What is the critical rho value at a 0.05 significance?
Do we have correlation?
In: Statistics and Probability
A company is considering three options for managing its data processing operation: continuing with its own staff, hiring an outside vendor to do the managing, or using a combination of its own staff and an outside vendor. There are three levels of demand under consideration: high, medium, and low. The annual profit associated with each option (in $1,000) for each level of demand is given below:
Demand Level
Staffing Options High Medium Low
Own staff 950 900 650
Outside vendor 850 650 500
Combination 1000 800 400
3. For the problem given above, the probabilities are given by P(high demand) = 0.4, P(medium demand) = 0.3, and P(low demand) = 0.3.
(a) Compute the expected value for each decision and select the best one.
(b) Compute the expected regret value for each decision and select the best one.
(c) Calculate and interpret the expected value of perfect information.
In: Statistics and Probability
Company A is preparing a deal to acquire company B. One analyst estimated that the merger would produce 175 million dollars of annual cost savings, from operations, general and administrative expenses and marketing. These annual cost savings are expected to begin two years from now, and grow at 2% a year. In addition the analyst is assuming an after-tax integration cost of 0.3 billion, and taxes of 20%. Assume that the integration cost of 0.3 billion happens right when the merger is completed (year 0). The analyst is using a cost of capital of 8% to value the synergies. Company B’s equity is trading at 2.3 B dollars (market value of equity). Given this, Company A is planning to pay a 30% premium for company B.
a) Compute the value of the synergy as estimated by the analyst. Please show your calculations.
| b) Does the estimate of synergies in a) justify the premium that company A offered to company B? (1 paragraph at most) |
In: Finance
The Video Game Supply Company (VGS) is deciding whether to set next year's production at 2000, 2500, or 3000 games. Demand could be low, medium, or high. Using historical data, VGS estimates the probabilities as: 0.4 for low demand, 0.3 for medium demand, and 0.3 for high demand. The following profit payoff table (in $100s) has been developed. Production Target Demand Low Medium High 2000 games 1000 1200 1400 2500 games 800 1500 1300 3000 games 600 1700 1400
[1] What is the maximax decision alternative? [1] What is the maximin decision alternative? [2] Determine the expected value of each alternative and indicate what should be the production target for next year based on expected value. [1] Determine the expected value with perfect information about the states of nature. [1] Determine the expected value of perfect information.
In: Statistics and Probability
The Video Game Supply Company (VGS) is deciding whether to set next year's production at 2000, 2500, or 3000 games. Demand could be low, medium, or high. Using historical data, VGS estimates the probabilities as: 0.4 for low demand, 0.3 for medium demand, and 0.3 for high demand. The following profit payoff table (in $100s) has been developed. Production Target Demand Low Medium High 2000 games 1000 1200 1400 2500 games 800 1500 1300 3000 games 600 1700 1400
[1] What is the maximax decision alternative? [1] What is the maximin decision alternative? [2] Determine the expected value of each alternative and indicate what should be the production target for next year based on expected value. [1] Determine the expected value with perfect information about the states of nature. [1] Determine the expected value of perfect information.
In: Statistics and Probability
Given:Ho:p≥0.4,Ha:p<0.4,n=25,RejectHo ifX≤7
(a) Find the level of significance .
(b) If in fact p = 0.3, what would be the probability of making a
type II error?
(c) If the true value of p were 0.3, find the probability the test
would detect that this is the case.
What is this probability called?
(d) Suppose that X is observed to be xo = 5.
(i) What is your decision? (ii) What type of error are you subject to? (iii)What is the P-value?
(e) By hand draw the power curve for this hypothesis test.
Include the table giving the values of K(p) for p = 0.05, 0.10,
0.20, ..., 0.90, 0.95 and indicate where is on your curve.
(f) For the hypotheses, Ho: p ≥ 0.4, Ha: p < 0.4, n = 25, set up a rejection region so that is as close as possible to, but does not exceed 0.10. State both the 'nominal' and the 'exact' .
In: Statistics and Probability
Company A is preparing a deal to acquire company B. One analyst estimated that the merger would produce 175 million dollars of annual cost savings, from operations, general and administrative expenses and marketing. These annual cost savings are expected to begin two years from now, and grow at 2% a year. In addition the analyst is assuming an after-tax integration cost of 0.3 billion, and taxes of 20%. Assume that the integration cost of 0.3 billion happens right when the merger is completed (year 0). The analyst is using a cost of capital of 8% to value the synergies.
Company B’s equity is trading at 2.3 B dollars (market value of equity). Given this, Company A is planning to pay a 30% premium for company B.
a) Compute the value of the synergy as estimated by the analyst. Please show your calculations.
b) Does the estimate of synergies in a) justify the premium that company A offered to company B? (1 paragraph at most)
In: Accounting
PROBLEM 1:
Sales records for the last six quarters for Howard Bakery which is
famous for its multi-grain bread are given below: (Sales data are
in thousands of pounds, but ignore the last three zeros for ease of
computation.)
Quarter Sales ($)
successive quarter.
In: Operations Management
1. Amy rolls 15 8-sided dice. What is the probability that at least 2 of the rolls are 5s?
Answer: 0.5759
2. Amy shoots 10 arrows at a target. Each arrow hits the target (independently) with probability 0.3. What is the probability that at least 3 of the arrows hit the target?
Answer: 0.6172
3. Amy shoots 64000 arrows at a target. Each arrow hits the target (independently) with probability 0.3. What is the probability that more than 2 of the first 17 arrows hit the target?
Answer: 0.9226
4. Amy tosses 19 biased coins. Each coin comes up heads with probability 0.1. What is the probability that at least 3 of the coins come up heads?
Answer: 0.2946
5. Amy tosses 10 biased coins. Each coin comes up heads with probability 0.5. What is the probability that at most 1 of the coins come up heads?
Answer: 0.0107
In: Statistics and Probability
School is interested in knowing the average height of undergraduate students but do not have time to measure all the students. 100 students were randomly selected and it is found that the average height of these 100 students is 1.60 metres with a standard deviation of 0.3 metres.
a) State the point estimate of the average height of undergraduate students.
b) Construct an interval estimate of the average height of students with 99% confidence.
c) The respond rate of the above survey was 85%, i.e. 85% of the students contacted were willing to participate in the survey. Construct an interval estimate of the proportion of students population who are willing to participate in other similar survey with 95% confidence.
d) The Student Services Centre is not very convinced of the result and would like to conduct a second survey. It would like to estimate the mean population height of students to be within 0.05 metres and be 99% confident, assuming the population standard deviation is 0.3 metres, how large a sample is necessary to achieve the accuracy stated?
In: Statistics and Probability