California University of PAName: Leslie Finney

BUS 381 001—Management Science II

Mr. Matthew Goodburn, Instructor

Final Exam--100 points

May 10, 2018

Section 1: Multiple Choice: Circle the best answer for the following questions. (1 point each)

  1. The model below was estimated to explain WAGE (hourly wage in dollars) as a function of EXPERIENCE (in years) and gender (MALE is a dummy variable = 1 for men, and 0 otherwise). Assuming that the dataset includes 100 observations, the t-statistics and p-values for each coefficient estimate appear in parentheses below the coefficients.

WAGE = 5.24 + 1.04*EXPERIENCE + 2.34*MALE
t-stat (1.12) (3.04)
p-value(0.231) (0.007)

At the 5% level of significance, which of the following statements is true?

  1. The coefficient on EXPERIENCE is not statistically significantly different from 0, while the coefficient on MALE is statistically significantly different from 0.
  2. Both of the coefficients are statistically significantly different from 0
  3. Neither of the coefficients are statistically significantly different from 0.
  4. The coefficient on EXPERIENCE is statistically significantly different from 0, while the coefficient on MALE is not statistically significantly different from 0.
  1. The overall significance of a regression model is tested using the F test. We will reject the null hypothesis and conclude that the model has statistically significant explanatory power if
  1. the estimated coefficients are very large.
  2. the R2 is low.
  3. the F statistic value is low (or the p-value is high).
  4. the F statistic has a p-value that is less than or equal to the level of significance, α.
  1. Which of the following are all measures of variation?
  1. Variance, standard deviation and range
  2. Mean, median and mode
  3. The first quartile and the third quartile
  4. Frequency, probability and histograms

  1. If correlation between two variables is near 0, then it implies that
  1. there exists a positive relationship between the variables.
  2. the variables are not linearly related.
  3. the variables are negatively related.
  4. the variables are strongly related.
  1. A useful type of table for describing data of two variables is a:
  2. Frequency distribution table.
  3. bubble chart.
  4. crosstabulation.
  5. scatter chart.
  6. A multiple regression model has ______dependent variable(s).
  1. one
  2. more than one
  3. at least 4 (or more)
  4. a maximum of 10
  5. between a range of 6 to a max of 15
  1. The charts that are helpful in making comparisons between categorical variables are:
  1. bar charts and scatter charts.
  2. scatter charts and line charts.
  3. column charts and line charts.
  4. bar charts and column charts.
  1. In designing an effective table,
  1. avoid the use of unnecessary ink in tables.
  2. increase the number of horizontal and vertical lines in the table.
  3. avoid the use of necessary ink in tables.
  4. do not focus on the alignment of the text and numbers in the table.
  1. The principle of using the simplest meaningful model possible without sacrificing accuracy is referred to as_____.
  1. Engel’s law
  2. KISS principle
  3. Murphy’s law
  4. Ockham’s razor
  1. The term _____ refers to the expression that defines the quantity to be maximized or minimized in a linear programming model.
  1. objective function
  2. problem formulation
  3. decision variable
  4. association rule

Section 2: True or False. Identify each of the following statements as true or false. If it is false, explain why or give a counter-example. (2 points each)

1. The data on grades (A, B, C, and D) scored by all students on a test is an example of quantitative data.

False

The data on grades (A,B,C, and D) scored by all students on a test is an example of categorical data.

2. Deleting the grid lines in the table and the horizontal lines in the chart increases the data-ink ratio.

True

3. The coefficient of determination always has a value between -1 and 1.

False

The coefficient of determination always has a value between zero and positive one.

4. A multiple regression analysis involves one dependent variable and more than one independent variable.

True

5. If the z-score (or z-value) for a variable X has a value of 2.47, then we can classify X as an outlier.

True

6. An objective solution satisfies all the constraint expressions simultaneously.

A feasible solution satisfies all the constraint expressions simultaneously.

Section 3: Matching: Match the terms in the left hand column with the definitions in the right hand column, by writing the number represent the term in column 1 in the blank line of the definition in column 2. (1 point each)

  1. R2
/ __3___ the estimated value of the slope parameter (or intercept) in a regression model
  1. residual (or error)
/ If two events (A, B) are mutually exclusive, the probability of event A and event B occurring is given by _____8_____.
  1. (beta-hat or b)
/ ___2__ the difference between the actual value and the predicted value
  1. dummy variable
/ __1___ percentage of variation in the Y variable that is explained by variation in the Xs
  1. Cross-sectional data
/ A __7___ is a graphical presentation of the relationship between two quantitative variables.
  1. P(A and B) = P(A) ∙P(B)
/ If two events (A, B) are independent, the probability of event A and event B occurring is given by ____6______.
  1. scatter chart
/ __5___ are collected from several entities at the same point in time.
  1. P(A and B) = 0
/ __4___ a variable that represents categorical data (using 0s and 1s)

Section 4: Problems: Answer each of the following problems.

  1. A production process is known to produce a particular item in such a way that 9% of these items are defective. If four items are randomly selected as they come off the production line, what is the probability that all four are NOT defective (assuming that they are all independent)? (5 points)

0.05*2+0.95*0.09

=0.19

  1. A manufacturing company produces two types of skis—a trick ski and a slalom ski. The trick ski requires 6 hours of labor for fabricating and 1 hour of labor for finishing. The slalom ski requires 4 hours of labor for fabricating and 1 hour of labor for finishing. The company has 108 hours per day for fabricating and 24 hours per day for finishing. The company makes $50 profit on each trick ski sold and $60 profit on each slalom ski sold. Assume the company can sell all of its output. The company is interested in maximizing the total profit, answer the following:
  1. What is the objective for this problem? Write it out formally. (2 points)

Objective Function: Profit= 50x + 60g

Goal: Maximize 50x + 60g

  1. What are the constraint functions for this problem? Write them out formally. (4 points)

For Fabricating: 6x + 4g < 108

Labor and Finishing: 1x +1g < 24

  1. Graph the constraints and shade the area that represents the feasible region. (6 points)

6x + 4g < 108If x=0, then g= 84(x,g) Point: (0,84)

If g=0, then x= 108(x,g) Point: (108,0)

1x + 1g < 24If x= 0, then g=192(x,g) Point: (0,192)

If g= 0, then x=84(x,g) Point: (84,0)

  1. How many skis of each model should be produced in order to maximize profits? (6 points)
  1. How many hours of production time will be scheduled in each department? (2 points)

Section 5: Excel Problems: Excel Problems: Open the Excel workbook FinalExam.xlsx which contains one worksheet, with two tabs. Use this workbook to answer the following questions. Place your answers in the workbook and save file as “Lastname_finalexam.xlsx”. Upload the file to the Final Exam dropbox on the course D2L shell.

1. The data set for problem 1 contains four variables—Reading SAT score, Math SAT score, Freshman GPA, and Gender (Female or Male)—for a random sample of 50 freshman at College University. A statistics professor wants to predict a freshman student’s GPA based on their incoming Reading SAT scores, Math SAT scores, and Gender.

  1. Calculate the sample mean and sample standard deviation for the Math SAT score variable. (5 points)
  1. Add a dummy variable to the data called “FEMALE.” Then estimate the multiple linear regression model predicting freshman GPA as a function of the SAT scores on the Reading and Math portions of the test, as well as gender (the FEMALE dummy variable). Write out the actual equation. (5 points)
  1. Use the F test to determine the overall significance of the regression relationship (that is, test the null hypothesis that β0 = β1 = β2 = β3 =0 versus the alternative that at least one of these is not equal to zero). What is the conclusion at the 0.05 level of significance? (5 points)
  1. Test to see if the Reading SAT score variable is significant at the 0.05 level. That is, test the null hypothesis that β1 =0 versus the alternative hypothesis that β1 ≠0. Is this variable significant? Explain your decision. (5 points)
  1. Test to see if the dummy variable FEMALE is significant at the 0.05 level. That is, test the null hypothesis that β3 =0 versus the alternative hypothesis that β3 ≠0. Is this variable significant? Explain your decision. (5 points)

2. For the GasNGo Company, the weekly sales of gasoline are given in the Excel table in the tab “Problem 2”, measured in thousands of gallons. Complete the following based on the values given in the table.

a. Using the naïve method (most recent value) as the forecast for the next week, compute the following measure of forecast accuracy:

i. Mean square error. (7 points)

ii. What is the forecast for week 13? (2 points)

b. Using a three-week moving average as the forecast for the next week, compute the following measure of forecast accuracy:

  1. Mean square error. (7 points)
  1. What is the forecast for week 13? (2 points)

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