Mathematics Assignment-Quant. Analysis
10) A company is considering producing some new Gameboy electronic games. Based on past records, management believes that there is a 70 percent chance that each of these will be successful, and a 30 percent chance of failure. Market research may be used to revise these probabilities. In the past, the successful products were predicted to be successful based on market research 90 percent of the time. However, for products that failed, the market research predicted these would be successes 20 percent of the time. If market research is performed for a new product, what is the probability that the product will be successful if the market research indicates a success?
A) 0.10
B) 0.90
C) 0.91
D) 0.63
E) 0.09
11) Which of the following is true about the expected value of perfect information?
A) It is the amount you would pay for any sample study.
B) It is calculated as EMV minus EOL.
C) It is calculated as expected value with perfect information minus maximum EMV.
D) It is the amount charged for marketing research.
E) None of the above
12) The following is a payoff table giving profits for various situations.
What decision would an optimist make?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) Do Nothing
E) State of Nature A
13) The following is an opportunity loss table.
What decision should be made based on the minimax regret criterion?
A) Alternative 1
B) Alternative 2
C) Alternative 3
D) State of Nature A
E) Does not matter
14) Dr. Mac, a surgeon, must decide what mode of treatment to use on Mr. Samuels. There are three modes of treatment: Mode A, B, and C; and three possible states of nature: 1. Treatment succeeds and patient leads a normal life, 2. Patient survives treatment but is permanently disabled, and 3. Patient fails to survive treatment. Dr. Mac has prepared the decision table below. What mode of treatment maximizes the expected value?
A) Mode A
B) Mode B
C) Mode C
D) All three treatments are equally desirable.
E) Normal Life
15) Bayes' theorem enables decision makers to revise probabilities based on
A) perfect information.
B) knowing, ahead of time, the actual outcome of the decision.
C) additional information.
D) measurements of utility.
E) None of the above
16) The saddle point in a payoff matrix is always the
A) largest number in its column and the largest number in its row.
B) largest number in its column and the smallest number in its row.
C) smallest number in its column and the largest number in its row.
D) smallest number in its column and the smallest number in its row.
E) None of the above
17) Consider the following two-person game. The payoff for X is given in the table. X will always play strategy
Y1 Y2
X1 4 6
X2 1 -3
A) X1.
B) X2.
C) Y1.
D) Y2.
E) Not enough information given
18) CleanClothes dry cleaners is opening a pick-up and delivery service. There is only one other dry cleaner that currently offers this service. To advertise, CleanClothes is considering either newspaper ads or attaching flyers to the doors of many local homes. The payoff for each of CleanClothes' potential strategies is given in the table below. What strategy will the existing dry cleaners (Y) play?
Y1 (newspaper ads) Y2 (flyers)
X1 (newspaper ads) 52 37
X2 (flyers) 26 18
A) X1
B) X2
C) Y1
D) Y2
E) Not enough information given
19) Considering the following two-person game, what percentage of the time should X play strategy X2?
Y1 Y2
X1 6 3
X2 2 8
A) 1/3
B) 2/3
C) 4/9
D) 5/9
E) None of the above
20) Given the following two-person game, which strategy can be eliminated by use of dominance?
Y1 Y2
X1 13 9
X2 6 8
X3 12 14
A) X1
B) X2
C) X3
D) Y1
E) Y2
21) Which of the following statements is true regarding a scatter diagram?
A) It provides very little information about the relationship between the regression variables.
B) It is a plot of the independent and dependent variables.
C) It is a line chart of the independent and dependent variables.
D) It has a value between -1 and +1.
E) It gives the percent of variation in the dependent variable that is explained by the independent variable.
22) The sum of squared error (SSE) is
A) a measure of the total variation in Y about the mean.
B) a measure of the total variation in X about the mean.
C) a measure in the variation of Y about the regression line.
D) a measure in the variation of X about the regression line.
E) None of the above
23) If computing a causal linear regression model of Y = a + bX and the resultant r2 is very near zero, then one would be able to conclude that
A) Y = a + bX is a good forecasting method.
B) Y = a + bX is not a good forecasting method.
C) a multiple linear regression model is a good forecasting method for the data.
D) a multiple linear regression model is not a good forecasting method for the data.
E) None of the above
24) The diagram below illustrates data with a
A) negative correlation coefficient.
B) zero correlation coefficient.
C) positive correlation coefficient.
D) correlation coefficient equal to +1.
E) None of the above
25) Which of the following statements provides the best guidance for model building?
A) If the value of r2 increases as more variables are added to the model, the variables should remain in the model, regardless of the magnitude of increase.
B) If the value of the adjusted r2 increases as more variables are added to the model, the variables should remain in the model.
C) If the value of r2 increases as more variables are added to the model, the variables should not remain in the model, regardless of the magnitude of the increase.
D) If the value of the adjusted r2 increases as more variables are added to the model, the variables should not remain in the model.
E) None of the statements provide accurate guidance.
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