# Quantatative Anaylisis Final

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See attachment for Quantitative analysis assignment. Make sure they provide all excel functions that are called out for in the problems, use equation editor in word and read all directions in the word document. On problem 4 it says “give LP model” that stands for Linear Programming Model.

Notes: All work should be done individually. Word-process your solutions within this template and show all steps used in arriving at the final answers. Incomplete solutions will receive partial credit. Copy and paste all necessary data from Excel into this document and create tables as needed.”

Problem 1

Throughout the 1990’s the average household expenditure on scratch tickets in a state has been \$5.  In 2010, a sample of 7 households was selected at random and the following expenditures for a given week were reported:

\$3, \$2, \$4, \$3, \$5, \$4, \$7

(a)    What is the sample mean expenditure for scratch tickets?

(b)   What is the sample standard deviation for the sample results?

(c)    What are the null and alternate hypotheses if we wished to test the hypothesis that the average    expenditure on scratch tickets has decreased in the 21st century?

(d)   What is the critical score which will determine your conclusion?

(e)   What is the computed score found from the sample data and what is your conclusion based on these results?

Problem 2

A store wishes to predict net profit as a function of sales for the next year.  The following table gives the years 1998 to 2005.

 Year Sales (thousands of dollars) Net Profit 1998 48 8.0 1999 52 9.4 2000 53 11.3 2001 78 8.6 2002 80 6.6 2003 70 4.1 2004 62 −1.0 2005 55 −2.0

(a)    Graph the points from 1998 through 2005 on a scatter diagram using Sales as the independent variable and Net Profit as the dependent variable.

(b)   Draw the regression line on the graph you constructed in Part (a).

(c)    What is the value of the coefficient of determination for this regression model? Comment on the strength of the regression line for this model.

(d)   What is the predicted net profit for 2006 if sales are expected to be 75?

Problem 3

The following table shows the last six years average new weekly unemployment insurance claims.

 Year Average weekly new unemployment insurance claims 2004 341,300 2005 333,600 2006 311,300 2007 321,200 2008 415,800 2009 567,600

(a)    Forecast the new weekly unemployment insurance claims for all years from 2007 to 2010. Use a three-year weighted moving average with weights of 0.6, 0.3, and 0.1. Use the largest weight with the most recent data.

(b)   Forecast the new weekly unemployment insurance claims using exponential smoothing with alpha = 0.6 for all years from 2005 to 2010. Use the rate for 2004 as the starting forecast for 2004.

(c)    Which of the methods in parts (a) and (b) produces better forecasts for the three years from 2007 to 2009? Answer on the basis of mean square error (MSE).

Problem 4

A financial services firm is opening a branch and they need to make staffing decisions. Administrative assistants are worth \$100 in weekly profit, but they require \$100 from the technology budget and 50 ft2 of office space.  Attorneys bring in \$2000 a week in profit, while using \$100 from the technology budget and 400 ft2 of office space.  Analysts are worth \$500 a week in profit and use \$1000 from the technology budget and 100 ft2 of office space.  Finally, the traders are worth \$1500 a week in profit, but require \$200 from the technology budget and 400 ft2 of space. The office needs to have at least 4 administrative assistants and 10 analysts.  There are only 4 attorneys available for the new office, and you can bring at most 50 people to the new branch.  The technology budget is \$20,000 per week, and the new office has 12,000 ft2 of space available. Give the LP Model and Excel Solver to find the optimal solution.

Problem 5

A company purchases its merchandise for \$10 and sells for each item for \$20. The pay-off table for the problem is given below.

 Demand for Item Alternative Low Medium High Do nothing 0 0 0 Order Low 30,000 30,000 30,000 Order Medium 10,000 50,000 40,000 Order High -10,000 40,000 80,000 Probability 0.3 0.3 0.4

What is the decision based on each of the following criteria?

(a)    EMV approach

(b)   EOL approach

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