Instructions:

1. Word-process your solutions or use Excel. If using Excel, use 1 spreadsheet and label each tab

with problems. DO NOT send multiple spreadsheets. 2. Show all steps used in arriving at the final answers. Incomplete solutions will receive partial

credit. 3. Use of software package is at your discretion. You can use any software package to solve

Problems 3 – 5. 4. Be sure to clearly show the answers to each question, software generated or your computation. 10 Total Points: True or False? 1 point each, please highlight your responses or use a different font color

a. Assume that the histogram of a data set is symmetric and bell shaped, with a mean of 75 and

standard deviation of 10. Then, approximately 95% of the data values were between 55 and 95.

b. A low p–value provides evidence for accepting the null hypothesis and rejecting the alternative.

A t-test is used to determine whether the coefficients of the regression model are significantly

different from zero.

d. Decision trees are more appropriate tools than decision tables when a sequence of decisions must

be made.

e. If a solution to an LP problem satisfies all of the constraints, then is must be feasible and

bounded.

f. Correlation is measured on a scale from 0 to 1, where 0 indicates no linear relationship between

two variables, and 1 indicates a perfect linear relationship.

g. In multiple regression, the problem of multicollinearity affects the t-tests of the individual

coefficients as well as the F-test in the analysis of variance for regression, since the F-test

combines these t-tests into a single test.

c. h. In a random walk model, there are significantly more runs than expected, and the

autocorrelations are not significant. i. When we maximize or minimize the value of a decision variable by running several simulations

simultaneously, we have found an optimal solution to the problem and attitude toward risk

becomes irrelevant. a. 1.` 2. 20 Total Points Multiple choice (2 Points each) Please highlight or clearly mark your responses

Expressed in percentiles, the interquartile range is the difference between the

a. 10th and 60th percentiles

b. 15th and 65th percentiles

c. 20th and 70th percentiles

d. 25th and 75th percentiles

e. 35th and 85th percentiles

Which of the following are considered measures of association?

a. Mean and variance

b. Variance and correlation c. Correlation and covariance

d. Covariance and variance

e. First quartile and third quartile

3. If A and B are mutually exclusive events with P(A) = 0.70, then P(B):

a. can be any value between 0 and 1

b. can be any value between 0 and 0.70

c. cannot be larger than 0.30

d. Cannot be determined with the information given 4. Sampling error is evident when:

a. a question is poorly worded

b. the sample is too small

c. the sample is not random

d. the sample mean differs from the population mean 5. After calculating the sample size needed to estimate a population proportion to within 0.05, you have

been told that the maximum allowable error (B) must be reduced to just 0.025. If the original calculation

led to a sample size of 1000, the sample size will now have to be:

a. 2000

c. 1000

b. 4000

d. 8000 6. A multiple regression analysis including 50 data points and 5 independent variables results in

The multiple standard error of estimate will be:

a. 0.901

b. 0.888

c. 0.800

d. 0.953

e. 0.894 7. In a random walk model the

a. series itself is random

b. series itself is not random but its differences are random

c. series itself and its differences are random

d. series itself and its differences are not random 8. When using exponential smoothing, if you want the forecast to react quickly to movements in the series,

you should choose:

a. values of

near 1

b. values of

near 0

c. values of

midway between 0 and 1

d. it depends on the data set 9. Consider the following linear programming problem:

Maximize

Subject to 40. The above linear programming problem:

a.

b.

c.

d.

10. has only one optimal solution

has more than one optimal solution

exhibits infeasibility

exhibits unboundedness The expected value of perfect information (EVPI) is equal to:

a. EMV with posterior information – EMV with prior information

b. EMV with free perfect information – EMV with information

c. EMV with free perfect information – EMV with no information

d. EMV with perfect information – EMV with less than perfect information Problem 3 (10 points)

Hunter Chemical Company claims that its major product contains on the average 4.0 fluid ounces of

caustic materials per gallon. It further states that the distribution of caustic materials per gallon is normal

and has a standard deviation of 1.3 fluid ounces.

a. What proportion of the individual gallon containers for this product will contain more than 5.0 fluid

ounces of caustic materials? b. A government inspector randomly selects 100 gallon-size containers of the product and finds the

mean weight of caustic material to be 4.5 fluid ounces per gallon. What is the probability of finding

the mean of a sample of 100 that is 4.5 or greater? Do you think the production process was

producing its usual level of caustic materials when this sample was taken? Problem 4 (10 points)

Southern Textiles wishes to predict employee wages by using the employee’s experience X 1 and the

employee’s education X2. Employees are categorized as having a college degree or not having a college

degree in their personnel files, so the variable “education” is a qualitative variable. Thus, X 2 is an

indicator (0, 1) variable. Data for the employees are given below:

Wages Y (Thousands

of dollars) Experience X1

(Months) 27.1

20.1

25.1

22.3

25.2 47.2

40.1

37.1

44.7

41.9 Education (College Degree

= 1, No College Degree =

0)

1

0

1

0

1 27.4

13.8

11.0

22.4

30.3

28.5

26.7

21.9

22.1

18.7

21.8

11.8

14.1

23.1

30.8 46.1

17.0

29.2

30.7

59.8

48.0

55.3

42.9

47.2

40.1

36.5

20.0

30.7

36.8

49.9 1

1

0

1

0

1

0

0

0

0

1

0

0

1

1 (Economics for Management and Economics, Watson, Billingsley, Croft and Huntsberger, Fifth Edition,

1993, Page 685)

(a) Copy and paste the data from this document to an Excel file. Select Wages as the dependent variable and experience and education as the independent variables. Conduct multiple regression using Excel.

Paste the output report below. Note: Follow the instructions given in module 5 to conduct simple

regression. At the step where you specify the input data range, instead of selecting the data for one

independent variable, select data for all the independent variables.

(b) Write the equation from the regression output report. If you are using symbols in the equation for the variables, do define the symbols before using the symbols in the equation.

(c) Provide a clear and complete interpretation of the coefficients b 1 and b2 in the equation. There is no need to interpret b0. Note: Use actual variable names and numbers in answering your question. b 1 and

b2 are slopes is not a sufficient answer.

(d) What is the value of R 2 for this model? Do you think that the model does a good job of explaining the variation in wages? Why or why not?

(e) Set up the hypotheses to test whether the model is significant. Is the regression model significant at 0.05 as the level of significance? What does this mean?

(f) Set up the hypotheses to test for each of the regression coefficients individually and perform the test at the 0.05 level of significance.

(g) What average wages do you predict for employees with college degrees and experience = 40 months? Interpret your prediction.

Problem 5 (10 points)

The accompanying data are the times (in seconds) that it took a sample of employees to assemble a toy

truck at a Cole Industries assembly plant. Assembly times are normally distributed. At the 10% level, can

we conclude that the mean assembly time for this toy truck is not equal to 3 minutes? Use H a: µ ≠ 180

seconds as the alternative hypothesis.

Data 190

176 180

174 181

183 208

188 198

165 199

198 Problem 6 (10 points)

The accompanying data indicate the number of mergers that took place in an industry over a 19-year

period.

Year

1

2

3

4

5

6

7

a) Mergers

23

23

31

23

32

32

42 Year

8

9

10

11

12

13 Mergers

64

47

96

125

140

160 Year

14

15

16

17

18

19 Mergers

150

165

192

210

250

300 Fit a least squares trend line to the merger data. b) What type of trend (linear or curved) might best fit to this time series?

c) Compute the forecast for year 20 based on the trend (linear or curved) that best fits the data? Problem 7 (10 points)

Create another problem similar to Problem 3, 4, 5, or 6 and provide solutions as well.